基础数学与应用数学教研室， 博士生导师
联系方式：010-
电子邮箱：miao_changxing@iapcm.ac.cn
苗长兴, 曾荣获国家杰出青年基金、于敏数理科学奖、中国工程物理研究院杰出专家、中国工程物理研究院科技创新一等奖，是我国自己培养的在国际偏微分方程领域有影响的杰出数学家。近年来在国际一流的学术刊物(如：CPAM、CMP、ARMA、MZ、JFA、JMPA、SIAM、AIHP、CPDE、PLMS等)上发表论文九十余篇, 主要贡献表现在调和分析、非线性色散方程的散射理论与流体动力学方程的数学理论等研究领域，解决了若干个具有国际影响的数学问题，得到了著名数学家Kenig、 Constantin等国际同行的高度评价。
先后出版了《调和分析及其在偏微分方程中的应用》、《偏微分方程的调和分析方法》、《非线性波动方程的现代方法》、《Littlewood-Paley理论及其在流体动力学方程中的应用》等四部专著。 对国内这一核心数学领域的研究与发展起到了基础性的作用.所领导的科研团队被国际数学联盟前主席Kenig称为“国际偏微分方程研究领域最具活力与影响力的团队之一”。与此同时, 培养了一批年轻有为的数学才俊，特别是博士生张晓轶（获2010年美国斯隆研究奖、美国普林斯顿高等研究院的Neumann followship）在质量临界的Schrodinger方程、博士后陈琼蕾在流体动力学方程、徐桂香、郑继强等在非线性色散方程的动力学行为研究领域取得了出色的研究成果。
一、主要从事的研究方向
1. 现代调和分析及其在几何测度论、 数论中的应用;
2. 非线性色散方程的散射理论.
3. 流体动力学方程的数学理论
二、代表性论著
(I)专著：
1.苗长兴.《调和分析及其在偏微分方程中的应用》 (第二版), 现代基础数学丛书No.89,科学出版社.2004.3.
2.苗长兴、张波著.《偏微分方程的调和分析方法》, 现代基础数学丛书No.117，科学出版社.2008.3
3.苗长兴著.《非线性波动方程的现代方法》，(第二版), 现代基础数学丛书No.133科学出版社.2010.4.
4.苗长兴、吴家宏、章志飞著.《Littlewood-Paley理论及其在流体动力学方程中的应用》， 现代基础数学丛书No.142科学出版社.2012.4.
5.苗长兴编著.《现代调和分析及其应用讲义》，高等教育出版社,2018.
(II)论文：
１．C. Miao, Global well-posedness for the compressible Navier-Stokes equations with the highly oscillating initial velocity, Comm. Pure Appl. Math., Vol. LXIII (2010) 1173–1224. (with Q. Chen and Z. Zhang)
２．C. Miao, A new Bernstein's Inequality and the 2D Dissipative Quasi-Geostrophic Equation, Comm. Math. Phys, 271(2007), 821-838, (with Q. Chen and Z. Zhang)
３．C. Miao, Well-posedness in critical spaces for the compressible Navier-Stokes equations with density dependent viscosities, Revista Matematica Iberoam., 26(2010), 915-946, (with Q. Chen and Z. Zhang)
４．C. Miao, The dynamics of the 3D radial NLS with the combined terms, Comm. Math. Phys., 318:3(2013), 767-808, (with G. Xu and L. Zhao)
５．C. Miao, On the global well-posedness for the Boussinesq system with horizontal dissipation, Commun. Math. Phys. 321, 33–67 (2013), (2013), (with X. Zheng)
６．C. Miao, On the regularity criterion of weak solution for the 3D viscous Magneto-hydrodyn- amics equations, Comm. Math. Phys. 284(2008), 919-930, (with Q. Chen and Z. Zhang)
7． C. Miao, The Beale-Kato-Majda criterion to the 3D Magneto-hydrodynamics equations, Comm. Math. Phys, 275(2007), 861-872, (with Q. Chen and Z. Zhang)
8．C. Miao, On the well-posedness of the ideal MHD equations in the Triebel- Lizorkin spaces, Arch. Rational Mech. Anal. 195(2010), 561-578, (with Q. Chen and Z. Zhang)
9. C. Miao, Sobolev space adapted to the Schrodinger operator with inverse-square potential , Math. Z. (2017), DOI 10.1007/s00209-017-1934-8 (with R.Killip, M.Visan, J.Zhang and J.Zheng).
10．C. Miao, Global well-posedness and scattering for the energy-critical, defocusing Hartree eq- uation for radial data, J. Funct. Anal., 253(2007), 605-627, (with G. Xu and L. Zhao)
11．C. Miao, Global well-posedness and scattering for the mass-critical Hartree equation with radial data, J. Math. Pures Appl., 91(2009) 49-79, (with G. Xu and L. Zhao)
12. C.Miao, The defocusing energy-supercritical NLS in four space dimensions, J.Functional Analysis, 267(2014), 1662-1724 (with J.Murphy and J.Zheng)
13. C. Miao, Global well-posedness for axisymmetric Boussinesq system with horizontal viscosity, J. Math. Pures Appl. 101 (2014) 842–872（with X. Zheng）
14. C. Miao, On the ill-posedness of the compressible Navier-Stokes equations in the critical Besov spaces, Revista Matemtica Iberoamericana, 31(2015)1375-1402 (with Q.Chen and Z.Zhang).
15. C. Miao, Global well-posedness and scattering for the defocusing H1/2-subcritical Hartree eq- uation in Rd, Ann. Inst. Henri Poincare-Nonlinear Analysis, 26(2009)1831–1852.(with G. Xu and L. Zhao)
16. C. Miao, On the uniqueness of weak solutions for the 3D Navier-Stokes equations, Ann. Inst. Henri Poincare-Nonlinear Analysis, 26(2009)2165–2180. (with Q. Chen and Z. Zhang )
17. C.Miao, Bilinear Kakeya-Nikodym averages of eigenfunctions on compact Riemannian surfaces, J. Functional. Analysis. 271(2016)2752-2775 (with C.Sogge, Y.Xi and J.Yang)
18. C. Miao, The defocusing quintic NLS in four space dimensions, Ann. Inst. Henri Poincare-Nonlinear Analysis, 34 (2017) 759–787 (B.Dodson, J.Murpth, and J.Zheng)
19. C. Miao, The defocusing energy-critical wave equation with a cubic convolution, Indiana University Mathematics Journal , 63(2014)993-1015 (with J. Zhang and J. Zheng)
20.C. Miao, Global well-posedness and scattering for the energy-critical, defocusing Hartree equation in R1+n, Comm. PDEs, 36(2011)729 - 776, (with G. Xu and L. Zhao)
21.C. Miao, Global regularity for the supercritical dissipative quasi-geostrophic equation with large dispersive forcing, Proc. London Math. Society, 106 (2013) 650–674, (with M. Cannone and L. Xue),
22. C. Miao, Dispersive estimates with geometry of finite type, Comm. PDEs, 37(2012), 729 - 776, (with W. Chen and X. Yao)
23. C. Miao, Well-posedness for viscous shallow water equations in critical spaces, SIAM. J. Math. Anal., 40(2008), 443 - 474, (with Q. Chen and Z. Zhang)
24. C. Miao, A losing estimate for the ideal MHD equations with application to Blow-up criterion, SIAM J. Math. Anal., 38 (2007), 1847-859, (with M. Cannone and Q. Chen)
25. C. Miao, About convergence of solutions of fractal Burgers equation toward rarefaction waves. SIAM. J. Math. Anal., 39(2008), 1536 - 1549, (with G. Karch and X. Xu).
26. C.Miao, The 2D incompressible Boussinesq equations with general critical dissipation， SIAM J.Math.Anal，46(2014) 3426 –3454.(with Q.Jiu, J.Wu and Z.Zhang)
27. C.Miao, Stability of the traveling waves for the derivative Schr\"{o}dinger equation in the energy space, Calculus of Variations and PDEs , 56:45(2017), Doi: 10.1007/s00526-017-1128-6 (with X.Tang and G.Xu)
28. C.Miao, On the 4D Nonlinear Schr\"odinger equation with combined terms under the energy threshold, Calculus of Variations and PDEs (2017) 56:179 (with T.Zhao and J.Zheng)
29. C.Miao, Strichartz estimates for wave equation with inverse square potential, Contemp. Math., Vol. 15, No. 6 (2013) 1350026 (29 pages) (with J. Zhang and J.Zheng).
30.C. Miao, On the well-posedness of a 2D nonlinear and nonlocal system arising from the dislocation, Contemp. Math., Vol. 16, No. 2 (2014) 1350021 (36 pages) (with D. Li and L. Xue)
31. C. Miao, Scattering theory for NLS below energy space in dimension two, Contemp. Math., Vol. 17, No. 6 (2015) 1450052 (37 pages) (with J.Zheng)
32. C. Miao, On the isentropic compressible Euler equations with adiabatic index $\gamma=1$, Pacific J. Math., 262:1(2013), 109-128. (with D. Li and X. Zhang).
33. C.Miao, Maximal estimates for Schrodinger equation with inverse-square potential， Pacific Journal of mathematics,273(2015)1-20, (with J. Zhang and J. Zheng)
34. C. Miao, Global well-posedness for the 3D rotating Navier-Stokes equations with highly oscillating initial data, Pacific J. Math., 262:2(2013), 263-283, (with Q. Chen and Z. Zhang)
35. C. Miao, Dynamics for the focusing, energy-critical nonlinear Hartree equation, Forum Mathematicum. 27 ,No. 2(2015), 373–447 (with Y.Wu and G.Xu)
36. C.Miao, On Wolff’s L^2-Kakeya maximal inequality in $R^3$, Forum Mathematicum. 27, No5(2015) 3035-3047 (with J.Yang and J.Zeng)
37. C.Miao, Sacttering theory for the radial H^{\frac12}-critical wave equation with a cubic convolution, J. of Diff. Equat. 259 (2015) 7199–7237.(with J.Zhang and J.Zheng)
39. C. Miao , Energy Scattering for a Klein-Gordon Equation with a Cubic Convolution, J. of Diff. Equat.,257(2014)2178-2224, (with J.Zheng)
40. C. Miao, Global well-posedness for a modified critical dissipative quasi-geostrophic equation，J. of Diff. Equat., 252 (2012), 792 - 818, (with L. Xue)
41. C. Miao，Global well-posedness for the micropolar fluid system in critical Besov spaces，J. of Diff. Equat., 252(2012), 2698 - 2724, (with Q. Chen).
42. C. Miao, A note on the cone restriction conjecture，Proc. AMS, 140(2012), 2091 - 2102,（with J. Zhang and J. Zheng）
43. C. Miao, On global solution to the Klein–Gordon–Hartree equation below energy space, J. of Diff. Equat., 250 (2011), 3418 - 3447, (with J. Zhang)
44. C. Miao, Global well-posedness for Schrodinger equation with derivative in H1/2 (R), J. of Diff. Equat., 251 (2011), 2164 - 2195, (with Y. Wu and G. Xu).
45. C. Miao, On the regularity of a class of generalized quasi- geostrophic equations, J. of Diff. Equat., 251(2011), 2789 – 2821, (with L. Xue)
46. C. Miao, Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrodinger equations of fourth order in dimensions $d\geq 9$, J. of Diff. Equat., 251 (2011), 3381 – 3402, (with G. Xu and L. Zhao)
47. C. Miao, The focusing energy-critical Hartree equation, J. of Diff. Equat., 246 (2009), 1139-1163, (with D. Li and X. Zhang)
48. C. Miao, Global wellposedness and scattering for the focusing energy-critical nonlinear Schrodinger equations of fourth order in the radial case, J. of Diff. Equat., 246 (2009), 3715 – 3749, (with G. Xu and L. Zhao)
49. C. Miao, Global well-posedness of the critical Burgers equation in critical Besov spaces, J. of Diff. Equat., 247(2009), 1673 --1693, (with G. Wu).
50. C. Miao, Low regularity solutions of two fifth-order KdV type equations, Journal D’ Analyse Mathematique, 107 (2009), 221-238, (with W. Chen, J. Li and J. Wu)
51. C. Miao, On the low regularity of the fifth order Kadomtsev–Petviashvili I equation, J. of Diff. Equat., 245(2008), 3433 - 3469 (with W. Chen and J. Li)
52. C. Miao, Existence theorem and blow-up criterion of smooth solutions to the two-fluid MHD equations in R3, J. of Diff. Equat., 239 (2007), 251 - 271, (with Q. Chen)
53. C. Miao, Global solutions of the Klein-Gordon-Schrodinger system with rough data in R2+1, J. of Diff. Equat., 227(2006), 365 – 405, (with G. Xu)
54. C. Miao, Factorization theorem for product Hardy spaces. Studia Mathematica 177(2006) 255-249.(with W.Chen and Y.Han)
55. C.Miao, Scattering theory for the defocusing fourth-order Schrodinger Equations, Nonlinearity 29 (2016) 692–736(with J.Zheng),
56. C. Miao, An improved maximal inequality for 2D fractional order Schr\"{o}dinger operators, Studia Mathematica, 230 (2015), 121-165. (with J.Yang and J.Zheng).
57. C.Miao, On local smoothing problems and Stein's maximal spherical means, Proc. of AMS, 145 (2017) 4269–4282 ( with J.Yang and J.Zheng).
58. Global well-posedness and scattering for nonlinear Schrodinger equations with combined nonlinearities, J.of Diff.Equat. 261(2016), 2881-2934 . (with X.Cheng and L.Zhao).
59. C.Miao, Regularity conditions for the suitable weak solutions of the Navier-Stokes system from its rotation form，Pacific J. Math. 288(2017), 189-216(Y.Wang)
60. C. Miao, The two-dimensional Euler equations in Yudovich type space and bmo-type space, Revista Matemtica Iberoamericana, (2017), (Q.Chen and X.Zheng)
61 Solitary waves for nonlinear Schr\"{o}dinger equation with Derivative, Contemp. Math., ( 2017), DOI: 10.1142/S0219199717500493, 27pp (X.Tang and G.Xu)
62. C.Miao, Scattering in $H^1$ for the intercritical NLS with an inverse-square potential, JDE, doi:10.1016/j.jde.2017.11.015(2018). (with J.Lu and J.Murphy),