Baoxiang Wang

Peking University , Professor Research Interests:Nonliear partial differential equationHarmonic analysisBanach function spaces

I am a Professor in the School of Mathematical Sciences at Peking University. My main subjects are nonlinear partial differential equations, real harmonic analysis and the theory of function spaces. I am interested in the dispersive equations such as nonlinear Schrodinger equation, nonlinear Klein-Gordon equation and KdV like equation. Navier-Stokes equation is also my favoriate subject. In Harmonic Analysis I like modulation spaces and Besov type spaces and their applications to nonlinear PDE. During 1990--2001, one of my main subject is Banach function spaces--Orlicz spaces.

  • Hebei University  Mathematics, Bachelor | 1983. 9--1987. 6

  • Harbin University of Scienece and Technology  Pure Mathematics,  Master |  1987.8--1990. 5

  • Institute of Applied Physics and Computational Mathematics  Applied Mathematics, Ph Doctor | 1990.8-1994.2

  • 1994--1995, Hebei University,  Assistant Professor of Mathematics,

  • 1995--1997, Hebei University, Associate Professor of Mathematics,

  • 1997--2001, Hebei University, Professor of Mathematics

  • 2002--Present, Peking University, Professor of Mathematics


Phone: 86 10 62755951 (O)

Email: wbx@pku.edu.cn

Address: LMAM, School of Mathematical Sciences, Peking University, Beijing 100871 China

Wang Baoxiang’s Publications

1. Baoxiang Wang,  Ill-posedness for the Navier-Stokes equation in critical Besov spaces,  Advances in Mathematics, 268 (2015), 350--372.

    2. Jinsheng Han, Baoxiang Wang, alphamodulation spaces (I) embedding, interpolation and algebra properties, J. Math. Soc. Japan, 66 (2014)  1315–1373.

3. Wang Baoxiang, Globally well and ill posedness for non-elliptic derivative Schrödinger equations with small rough data.  J. Funct. Anal., 265 (2013), 3009–3052.

4. Ruzhansky,M. Sugimoto M., Wang B.X.,  Modulation and nonlinear  evolution equations, Progr. Math. 301,Birkhäuser/Springer Basel AG, Basel,  2012, 267-283.

5.Han,Lijia; Wang,Baoxiang; Guo,Boling Inviscid limit for the derivative Ginzburg-Landau equation withsmall data in modulation and Sobolev spaces.Appl. Comput. Harmon. Anal. 32(2012),no.2, 197–222.

6.  Hajaiej,Hichem; Molinet,Luc; Ozawa,Tohru; Wang,Baoxiang Necessary and sufficient conditions for the fractionalGagliardo-Nirenberg inequalities and applications to Navier-Stokes andgeneralized boson equations. Harmonic analysis and nonlinear partialdifferential equations, 159-175, RIMSKôkyûroku Bessatsu,  B26, Res. Inst. Math. Sci.  (RIMS), Kyoto,  2011.

7.  Wang,Baoxiang; Huo,Zhaohui; Hao,Chengchun; Guo,Zihua Harmonic analysis method for nonlinear evolution equations. I.WorldScientific Publishing Co. Pte. Ltd., Hackensack, NJ,  2011. 283 pp.

8.  Guo,Zihua; Peng,Lizhong; Wang,Baoxiang; Wang,Yuzhao Uniform well-posedness and inviscid limit for theBenjamin-Ono-Burgers equation.Adv.Math. 228(2011),no.2, 647–677.

9.  Sugimoto,Mitsuru; Tomita,Naohito; Wang,Baoxiang Remarks on nonlinear operations on modulation spaces.Integral Transforms Spec. Funct. 22(2011), no.4-5, 351–358.

10.     Feichtinger,Hans G.; Huang,Chunyan; Wang,Baoxiang Trace operators for modulation, α-modulation and Besov spaces.Appl. Comput. Harmon. Anal. 30(2011),no.1, 110–127.

11.  Guo,Zihua; Peng, Lizhong; Wang, Baoxiang On the local regularity of the KP-Iequation in anisotropic Sobolev space. J. Math. Pures Appl. (9) 94 (2010), no.4, 414–432,  

12.  Wang,Baoxiang; Han, Lijia; Huang, Chunyan Global well-posedness and scattering forthe derivative nonlinear Schrödinger equation with small rough data. Ann. Inst.H. Poincaré Anal. Non Linéaire 26 (2009), no. 6, 2253–2281.  

13.  Guo,Zihua; Wang, Baoxiang Global well-posedness and inviscid limit for theKorteweg-de Vries-Burgers equation. J. Differential Equations 246 (2009), no.10, 3864–3901.

14.  Han, Lijia; Wang, Baoxiang Globalwellposedness and limit behavior for the generalized finite-depth-fluidequation with small data in critical Besov spaces $\dot B{}^s_{2,1}$B˙s2,1. J.Differential Equations 245 (2008), no. 8, 2103–2144.

15.  Huang, Chunyan; Wang, Baoxiang Inviscidlimit for the energy-critical complex Ginzburg-Landau equation. J. Funct. Anal.255 (2008), no. 3, 681–725.

16.  Guo, Zihua; Peng, Lizhong; Wang, BaoxiangDecay estimates for a class of wave equations. J. Funct. Anal. 254 (2008), no.6, 1642–1660.

17.  Wang Baoxiang and Huang Chunyan, Frequenceuniform decomposition method for the KdV, BO and NLS, J. Differential Equations239 (2007), 213—250

18.  Tan, Shaobin and Wang, Baoxiang, On theoccasion of the seventieth birthday of Professor Guo Boling, J. PartialDifferential Equations 20 (2007), no. 1, 1--10;

19.  Hao, Chengchun, Hsiao, Ling and Wang,Baoxiang, Well-posedness of Cauchy problem for the fourth order nonlinearSchrodinger equations in multi-dimensional spaces, J. Math. Anal. Appl. 328(2007), no. 1, 58--83.

20.  Wang, Baoxiang and Hudzik, Henryk, Theglobal Cauchy problem for the NLS and NLKG with small rough data, J.Differential Equations 232 (2007), 36--73.  

21.  Wang, Baoxiang, Hao, Chengchun and Hudzik,Henryk, Energy scattering theory for the nonlinear Schrodinger equations withexponential growth in lower spatial dimensions, J. Differential Equations 228(2006), no. 1, 311--338.

22.  Wang, Baoxiang, Concentration phenomenonfor the $L^2$ critical and super critical nonlinear Schrodinger equations inenergy spaces, Commun. Contemp. Math. 8 (2006), no. 3, 309--330.

23.  Hao, Chengchun, Hsiao, Ling and Wang,Baoxiang, Wellposedness for the fourth order nonlinear Schrodinger equations,J. Math. Anal. Appl. 320 (2006), no. 1, 246--265;  

20.  Baoxiang, Wang, Lifeng, Zhao and Boling,Guo, Isometric decomposition operators, function spaces $E^_p,q$ andapplications to nonlinear evolution equations, J. Funct. Anal. 233 (2006), no.1, 1--39;  

21.  Wang, Baoxiang, Exponential Besov spacesand their applications to certain evolution equations with dissipation, Commun.Pure Appl. Anal. 3 (2004), no. 4, 883—919.

22.  Wang, Baoxiang, Guo, Boling and Zhao,Lifeng, The global well-posedness and spatial decay of solutions for thederivative complex Ginzburg-Landau equation in $H^1$, Nonlinear Anal. 57 (2004),no. 7-8, 1059—1076.

23.  Wang, Baoxiang, Nonlinear scattering theoryfor a class of  wave equations in $H^s$,J. Math. Anal. Appl. 296 (2004),  no. 1,74--96;

24.  Baoxiang, Wang and Youde, Wang, Theinviscid limit of the derivative complex Ginzburg-Landau equation, J. Math.Pures  Appl. (9) 83 (2004), no. 4,477--502;

25.  Wang, Bao Xiang, On the duality mappingsets in Orlicz  sequence spaces [1891750](Chinese), Acta Math. Sinica (Chin. Ser.) 46 (2003), no. 6, 1239--1242;

26.  Wang, Baoxiang, The Cauchy problem for the nonlinearSchrodinger equations involving derivative terms in one spatial dimension,Comment. Math., 43 (2003), no. 2, 275--300;

27.  Wang, Baoxiang and Hudzik, Henryk, On theduality mapping sets in abstract $M$-spaces, Indag. Math. (N.S.) 13  (2002),  1--9.

28.  Guo, Bo Ling and Wang, Bao Xiang,Scattering theory in $H^s$ for nonlinear Schrodinger equations (Chinese),Chinese  Ann. Math. Ser. A 24 (2003), no.3, 377—388.

29.  Wang, Baoxiang, Large time behavior ofsolutions for critical and subcritical complex Ginzburg-Landau equations in$H^1$, Sci. China Ser. A 46 (2003), no. 1, 64—74.

30.  Wang, Baoxiang, Bessel (Riesz) potentialson Banach function spaces and their applications. II. On existence of solutionsfor a class of nonlinear evolution equations, Nonlinear Anal. 47 (2001), no. 6,4283—4294.

31.  Baoxiang, Wang, The Cauchy problem forcritical and subcritical semilinear parabolic equations in $L^r$. II. Initialdata in critical Sobolev spaces $H^-s,r^s$, Nonlinear Anal. 52 (2003), no. 3,851—868.

32.  Wang, Bao Xiang, The smoothness ofscattering operators for sinh-Gordon and nonlinear Schrodinger equations, Acta Math.Sin. (Engl. Ser.) 18 (2002), no. 3, 549—564.

33.  Guo, Boling and Wang, Baoxiang, The globalCauchy problem and scattering of solutions for nonlinear Schrodinger equationsin $H^s$, Differential Integral Equations 15 (2002), no. 9, 1073—1083.

34.  Wang, Bao Xiang and Huo, Zhao Hui, TheCauchy problem for fourth-order Ginzburg-Landau equations (Chinese), ChineseAnn. Math. Ser. A 23 (2002), no. 2, 153—164.

35.  Wang, Bao Xiang, On the duality mappingsets in Orlicz sequence spaces, Acta Math. Sin. (Engl. Ser.) 17 (2001), no. 4,595—602.

36.  Wang, Baoxiang, The limit behavior ofsolutions for the Cauchy problem of the complex Ginzburg-Landau equation, Comm.Pure Appl. Math. 55 (2002), no. 4, 481—508.

37.  Baoxiang, Wang, The Cauchy problem forcritical and subcritical semilinear parabolic equations in $L^r$. I,  Nonlinear Anal. 48 (2002), no. 5, Ser. A:Theory Methods, 747—764.

38.  Wang, Baoxiang and Guo, Boling, On theinitial value problem and scattering of solutions for the generalizedDavey-Stewartson systems, Sci. China Ser. A 44 (2001), no. 8, 994—1002.

39.  Wang, Baoxiang, On the initial-boundaryvalue problems for nonlinear Schrodinger equations, Adv. Math. (China) 29(2000), no. 5, 421—424.

40.  Baoxiang, Wang, On weakly convergentsequences in Banach function spaces and the initial-boundary value problems fornon-linear Klein-Gordon-Schrodinger equations, Math. Methods  Appl. Sci. 23 (2000), no. 18, 1655—1665.

41.  Li, Min Li, Wang, Bao Xiang and Wang, TingFu, Strongly exposed points of Orlicz sequence spaces (Chinese), Acta Math.Sinica (Chin. Ser.) 42 (1999), no. 4, 645—648.

42.  Wang, Baoxiang, Scattering of solutions forcritical and subcritical nonlinear Klein-Gordon equations in $H^s$,  Discrete Contin. Dynam. Systems 5 (1999), no.4,  753—763.

43.  Guo, Boling and Wang, Baoxiang, The Cauchyproblem for Davey-Stewartson systems, Comm. Pure Appl. Math. 52  (1999), no. 12, 1477—1490.

44.  Hudzik, Henryk and Wang, Baoxiang, Oncompactness of the duality mapping sets in Orlicz spaces, Nonlinear Anal. 38(1999), no. 4, Ser. A: Theory Methods, 417—433.

45.  Li, Minli, Wang, Baoxiang and Wang, Tingfu,Strongly exposed points of Orlicz sequence spaces, Acta Math. Sinica  (N.S.) 14 (1998), suppl., 593—604.

46.  Lu, Yanming and Wang, Baoxiang, Nonlinearsmall data scattering for higher order wave equations, in Nonlinear partialdifferential equations and applications (Chongqing, 1997), 134--140, World Sci.Publ., River Edge, NJ, 1998.

47.  Wang, Baoxiang, Bessel (Riesz) potentialson Banach function spaces and their applications. I. Theory, Acta Math. Sinica(N.S.) 14 (1998), no. 3, 327—340.

48.  Wang, Bao Xiang, Bessel (Riesz) potentialson Banach function spaces and their applications. I. Theory (Chinese),  Acta Math. Sinica (Chin. Ser.) 41 (1998), no.5, 1007—1012.

49.  Hudzik, Henryk and Wang, Baoxiang, On thesmallest singular seminorm in a class of normed Kothe function spaces, Comment.Math.  38 (1998), 43—52.

50.  Hudzik, Henryk and Wang, Baoxiang,Approximate compactness in Orlicz spaces, J. Approx. Theory 95 (1998), no. 1,82—89.

51.  Wang, Baoxiang, The global Cauchy problemfor the critical and subcritical nonlinear Schrodinger equations in $H^s$, J.Partial Differential Equations 11 (1998), no. 2, 173—192.

52.  Wang, Baoxiang and Wang, Tingfu, Thecharacteristic of weak convergence on Banach sequence lattices, Collect. Math.48 (1997), no. 4-6, 799—807.

53.  Wang, Baoxiang, On existence and scatteringfor critical and subcritical nonlinear Klein-Gordon equations in $H^s$,Nonlinear Anal. 31 (1998), no. 5-6, 573—587.

54.  Wang, Baoxiang and Wang, Tingfu, Supportfunctionals and smooth points in abstract $M$ spaces, Proc. Amer. Math. Soc.127 (1999), no. 6, 1761—1770.

55.  Tingfu, Wang, Baoxiang, Wang and Liang,Zhao, On weakly (weakly$^*$) exposed points of Orlicz sequence spaces,Acta  Sci. Math. (Szeged) 63 (1997), no.3-4, 533—550.

56.  Baoxiang, Wang, Tingfu, Wang and Cuixia,Hao, On the WM property of Orlicz sequence spaces endowed with the Orlicz norm,Comment. Math. Univ. Carolin. 38 (1997), no. 1, 1-13.

57.  Baoxiang, Wang, Classical global solutionsfor non-linear Klein-Gordon-Schrodinger equations, Math. Methods Appl. Sci. 20(1997), no. 7, 599—616.

58.  Wang, Baoxiang and Xu, Meilan, On someapplications of support functionals in Orlicz spaces, Comment. Math. Prace  Mat. 35 (1995), 235—244.

59.  Wang, Ting Fu, Wang, Bao Xiang and Li, MinLi, lambda-coefficient of Orlicz sequence spaces, Colloq. Math. 69 (1995), no. 2,179—186.

60.  Wang, Bao Xiang and Wnuk, Witold, On semi-bounded modular spaces, Comment. Math. Prace Mat. 34 (1994), 229—235.

61.  Wang, Bao Xiang, Support functional and itsapplications in Orlicz spaces, Comment. Math. Prace Mat. 33 (1993), 185—192.

62.  Hudzik, Henryk, Wang, Bao Xiang and Wang,Ting Fu, On the convexity characteristic of Orlicz spaces, Math. Japon. 37 (1992),no. 4, 691—699.

Conferences:

1.      2000, World Congress of Nonlinear Analysts,Cartania, Italy, one hour speaker

2.      2004 World Congress of Nonlinear Analysts, Orlando, US,one hour speaker and organizer

3.      2006, International Conference on FunctionSpaces VIII, Poznan,plenary speaker (50 minutes),

4.      2008, World Congress of Nonlinear Analysts,Orlando, US, one hour speaker and organizer

5.      2008, Pseudo-Differential Operators andRelated Topics II, Vaxjo, plenary speaker (30 minutes),

6.      2009, Workshop on Differential Equations, Nagoya University, invited lecture (50 minutes)

7.      2009, International Conference on FunctionSpaces IX, Krakow,  plenary speaker (50 minutes)

8.      2009, The 9th internationalconference by graduate school of mathematics, Nagoya University—HarmonicAnalysis and Partial Diff Equation, Invited lecture (50 minites)

9.      2010, June  14—17, Workshop"Fourier Analysis and Partial Differential Equations",  Gottingen Unicersity,  Invited lecture (50 minites)

10.  2010, July 5—7,  RIMS Symposium ``Harmonic Analysis and Nonlinear PDE" , Kyoto University, Invited lecture (50 minites)

11. 2011, March 7--11 "Hyperbolic partial Differential Equations",  Imperial College London, Invited talk (50 minutes)

12. 2012 August 9--13, International Function Spaces X, Poznan 2012 (40 minutes plenary lecture)

13. 2013 July 6-8, Workshop on "Harmonic Analysis and Nonlinear PDE", Kyoto, RIMS (2 hour lecture)

14. 2013 August 5-9, ISAAC Congress 2013, Krakow (50 minutes plenary lecture)

Visits:

1995, A.Mickiewicz University, Professor Hudzik

2001, The University of Chicago, Professor Carlos E Kenig

2005, Chinese University of Hong Kong, Professor Zhouping Xin

2006, A.Mickiewicz University, Professor Hudzik

2008, Princeton University, Professor S. Klainerman

2009,Vienna University,Professor H. G. Fechtinger

2009,Nagoya University,Professor M. Sugimoto

2009, Kyoto University, Professor K. Nakanishi

2010, ToursUniversity, Professor L. Molinet

2013,  Kyoto University, Professor Y. Tsutsumi

2014,  Kyoto University, Professor Y. Tsutsumi

2014,  Imperial College London, Professor M. Ruzhansky


Journals:

2005---2008, EditoralBoard, Front. Math. China

2006---, Reviewerof Mathematical Review

2010,3 --,Advances of Math in China,Associte Editor in Chief

2010, 5--, Journalof Partial Differential Equations, Member of Editorial Board

2014,1--Fasciculi  Math. Member of Editorial Board

Yueling Jia: Institute of Applied Physics and Computational Mathematics, Associate Professor (Master student 1998-2000)

Zhaohui Huo: Institute of Mathematics, Chinese Academy of Sciences, Associate Professor (Master student 1998-2000)

Chengchun Hao: Institute of Mathematics, Chinese Academy of Sciences, Associate Professor (Master student 1999-2001)

Caixia Shen: Jiang Su University, Associate Professor (Master student 1999-2001)

Xiuqing Chen: Beijing Youdian University,  Associate Professor(Master student during 2000-2003)

Lifeng Zhao Chinese University of Science and Technology, Associate Professor (Ph D. 2002-2007, Joint with Prof Weiyue Ding)

Chunyan Huang: Central University of Finac., Ph D. 2003-2006

Lijia Han: North Central University of Elect., Associate Professor, Ph D 2004-2009

Zihua Guo: Peking University, Associate Professor, Ph D 2004-2009 (Joint with Profs Carlos Kenig and Lizhong Peng)

Yuzhao Wang: North Central University of Elect., Associate Professor, Ph D 2005-2010 (Joint with Prof Carlos Kenig)

Shuxia Wang, Ph D 2009-2013 (Joint with Prof Kenji Nakanishi)

Rongrong Zhang, Master 2010-2013

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