基础数学与应用数学教研室-苗长兴
所在单位：北京应用物理与计算数学研究所
导师职称：研究员，博士生导师
电子邮箱：miao_changxing@iapcm.ac.cn
招生专业：基础数学,应用数学
研究方向：现代调和分析及其在几何测度论、 数论中的应用；非线性色散方程的散射理论；流体动力学方程的数学理论
教育经历
工作经历
研究方向简介
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
个人荣誉、所获奖项等
代表性研究成果
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.
代表性论文：
[1] C.Miao, Forward self-similar solutions of the fractional Navier-Stokes Equations, Advances in Mathematics, 352(2019),981-1043.(with B.Lai and X.Zheng)
[2] C. Miao, Sobolev space adapted to the Schrodinger operator with inverse-square potential , Math. Z. (2018) 288:1273-1298 (with R.Killip, M.Visan, J.Zhang and J.Zheng).
[3] C.Miao, The energy-critical nonlinear wave equation with an inverse-square potential Ann. Inst. Henri Poincare-Nonlinear Analysis, 37 (2020) 417-456 (with J.Murpth, and J.Zheng)
[4] C.Miao, The defocusing energy-supercritical NLS in four space dimensions, J.Functional Analysis, 267(2014), 1662-1724 (with J.Murphy and J.Zheng)
[5] C. Miao, Global well-posedness for axisymmetric Boussinesq system with horizontal viscosity, J. Math. Pures Appl. 101 (2014) 842–872(with X. Zheng)
[6] 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).
[7] 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)
[8] 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 )
[9] 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)
[10] 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)
[11] 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)
[12] 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)
[13] 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),
[14] C. Miao, Dispersive estimates with geometry of finite type, Comm. PDEs, 37(2012), 729 - 776, (with W. Chen and X. Yao)
[15] 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)
[16] 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)
[17] 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).
[18] 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)
[19] C.Miao, Stability of the traveling waves for the derivative Schrödinger 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)
[20] 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).
[21] 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)
[22] 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)
[23] 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).
[24] 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)
[25] 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)
[26] 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)
[27] 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)
[28] 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)
[29] C. Miao , Energy Scattering for a Klein-Gordon Equation with a Cubic Convolution, J. of Diff. Equat.,257(2014)2178-2224, (with J.Zheng)
[30] C. Miao, Global well-posedness for a modified critical dissipative quasi-geostrophic equation，J. of Diff. Equat., 252 (2012), 792 - 818, (with L. Xue)
[31] 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).
[32] C. Miao, A note on the cone restriction conjecture，Proc. AMS, 140(2012), 2091 - 2102,(with J. Zhang and J. Zheng)
[33] 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)
[34] 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).
[35] C. Miao, On the regularity of a class of generalized quasi- geostrophic equations, J. of Diff. Equat., 251(2011), 2789 – 2821, (with L. Xue)
[36] 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)
[37] C. Miao, The focusing energy-critical Hartree equation, J. of Diff. Equat., 246 (2009), 1139-1163, (with D. Li and X. Zhang)
[38] 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)
[39] 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).
[40] 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)
[41] 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)
[42] 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)
[43] 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)
[44] C. Miao, Factorization theorem for product Hardy spaces. Studia Mathematica 177(2006) 255-249.(with W.Chen and Y.Han)
[45] C.Miao, Scattering theory for the defocusing fourth-order Schrodinger Equations, Nonlinearity 29 (2016) 692–736(with J.Zheng),
[46] C. Miao, An improved maximal inequality for 2D fractional order Schrödinger operators, Studia Mathematica, 230 (2015), 121-165. (with J.Yang and J.Zheng).
[47] 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).
[48] C.Miao, 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).
[49] 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( with Y.Wang)
[50] Solitary waves for nonlinear Schrödinger equation with Derivative, Contemp. Math., Vol. 20, No. 4 (2018) 1750049. (X.Tang and G.Xu)
[51] C.Miao, Scattering in H1 for the intercritical NLS with an inverse-square potential, JDE, 264(2018), 3174–3211. (with J.Lu and J.Murphy).
[52] C. Miao, The two-dimensional Euler equations in Yudovich type space and bmo-type space, Revista Matemtica Iberoamericana, 195–240. (with Q.Chen and X.Zheng)
[53] C. Miao, Linear adjoint restriction estimates for paraboloid, Math. Z. 292(2019) 427-451.( with J.Zhang and J.Zheng)
[54] C.Miao, On the regularity issues of a class of drift-diffusion equations with nonlocal diffusion. SIAM. J.Math.Anal. Vol. 51, 4(2019) 2927—2970. (with L. Xue)
[55] C. Miao, Square function inequality for a class of Fourier integral operators satisfying cinematic curvature conditions, Forum Math, 2020, (with C. Gao and J. Yang)
[56] C. Miao, Global well-posedness for the defocusing Hartree equation with radial data in R4 Communications in Contemporary Mathematics, Vol. 22, No. 2 (2020) 1950004 (35 pages) (with G.Xu and J.Yang)
[57] C. Miao,The global well-posedness and scattering for the 5-dimensional defocusing congormal invariant NLW with radial initial data in a critical Besov space, Pacific Journal of Mathematics, 305(1),2020, 251-290.( J. Yang and T.Zhao)