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邓稼先创新研究中心

《现代调和分析及其应用》研究团队介绍

一、 二、翻看上一页

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三、 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) 学术论文:

1. Q. Chen, C. Miao and Z. Zhang, Global well-posedness for the compressible Navier-Stokes equations with the highly oscillating initial velocity, Comm. Pure Appl. Math., Vol. LXIII (2010), 1173–1224.

2. Q. Chen, C. Miao and Z. Zhang, A new Bernstein's Inequality and the 2D Dissipative Quasi-Geostrophic Equation, Comm. Math. Phys, 271(2007), 821-838.

3. Q. Chen, C. Miao and Z. Zhang, Well-posedness in critical spaces for the compressible Navier-Stokes equations with density dependent viscosities, Revista Matematica Iberoam., 26(2010), 915-946.

4. C. Miao, G. Xu and L. Zhao, The dynamics of the 3D radial NLS with the combined terms, Comm. Math. Phys., 318:3(2013), 767-808.

亿博下载地址 5. C. Miao and X. Zheng, On the global well-posedness for the Boussinesq system with horizontal dissipation, Commun. Math. Phys. 321, 33–67 (2013).

亿博下载地址 6. Q. Chen, C. Miao and Z. Zhang, On the regularity criterion of weak solution for the 3D viscous Magneto-hydrodyn- amics equations, Comm. Math. Phys. 284(2008), 919-930,

亿博下载地址 7. Q. Chen, C. Miao and Z. Zhang, The Beale-Kato-Majda criterion to the 3D Magneto-hydrodynamics equations, Comm. Math. Phys, 275(2007), 861-872.

亿博下载地址 8. H. Jia, B. Liu and G. Xu, Long time dynamics of defocusing energy critical 3+1 dimensional wave equation with potential in the radial case, Comm. Math. Phys., 339(2015), 353-384.

9. Q. Chen, C. Miao and Z. Zhang, On the well-posedness of the ideal MHD equations in the Triebel- Lizorkin spaces, Arch. Rational Mech. Anal. 195(2010), 561-578.

10. R. Killip, C. Miao, M. Visan, J. Zhang and J. Zheng, Sobolev space adapted to the Schrodinger operator with inverse-square potential , Math. Z. (2017), doi: 10.1007/s00209-017-1934-8.

11. H. Jia, B. Liu, W. Schlag and G. Xu Generic and non-generic behavior of solutions to defocusing energy critical wave equation with potential in the radial case, IMRN, 2016, 1-59.

12. C. Miao, G. Xu and L. Zhao, Global well-posedness and scattering for the energy-critical, defocusing Hartree eq- uation for radial data, J. Funct. Anal., 253(2007), 605-627.

亿博下载地址 13. C. Miao, G. Xu and L. Zhao, Global well-posedness and scattering for the mass-critical Hartree equation with radial data, J. Math. Pures Appl., 91(2009) 49-79.

14. C. Miao, J. Murphy and J. Zheng, The defocusing energy-supercritical NLS in four space dimensions, J. Funct. Anal., 267(2014), 1662-1724.

15. C. Miao and X. Zheng, Global well-posedness for axisymmetric Boussinesq system with horizontal viscosity, J. Math. Pures Appl. 101 (2014) 842–872.

16. Q. Chen, C. Miao and Z. Zhang, On the ill-posedness of the compressible Navier-Stokes equations in the critical Besov spaces, Revista Matemtica Iberoamericana, 31(2015)1375-1402.

17. C. Miao, G. Xu and L. Zhao, 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.

亿博下载地址 18. Q. Chen, C. Miao and Z. Zhang, On the uniqueness of weak solutions for the 3D Navier-Stokes equations, Ann. Inst. Henri Poincare-Nonlinear Analysis, 26(2009)2165–2180.

亿博下载地址 19. C. Miao, C. Sogge, Y. Xi and J. Yang, Bilinear Kakeya-Nikodym averages of eigenfunctions on compact Riemannian surfaces, J. Func. Anal, 271(2016), 2752-2775.

亿博下载地址 20. B. Dodson, C. Miao, J. Murphy and J. Zheng, The defocusing quintic NLS in four space dimensions, Ann. Inst. Henri Poincare-Nonlinear Analysis, 34 (2017), 759–787.

21. C. Miao, J. Zhang and J. Zheng, The defocusing energy-critical wave equation with a cubic convolution, Indiana University Mathematics Journal, 63(2014), 993-1015.

亿博下载地址 22. C. Miao, G. Xu and L. Zhao, Global well-posedness and scattering for the energy-critical, defocusing Hartree equation in R1+n, Comm. PDEs, 36(2011)729 - 776.

亿博下载地址 23. M. Cannone, C. Miao and L. Xue, Global regularity for the supercritical dissipative quasi-geostrophic equation with large dispersive forcing, Proc. London Math. Society, 106 (2013), 650–674.

24. W. Chen, C. Miao and X. Yao, Dispersive estimates with geometry of finite type, Comm. PDEs, 37(2012), 729 - 776.

亿博下载地址 25. Q. Chen, C. Miao and Z. Zhang, Well-posedness for viscous shallow water equations in critical spaces, SIAM. J. Math. Anal., 40(2008), 443 - 474.

26. M. Cannone, Q. Chen and C. Miao, A losing estimate for the ideal MHD equations with application to Blow-up criterion, SIAM J. Math. Anal., 38 (2007), 1847-859.

27. G. Karch, C. Miao and X. Xu, About convergence of solutions of fractal Burgers equation toward rarefaction waves. SIAM. J. Math. Anal., 39(2008), 1536 - 1549.

28. Q. Jiu, C. Miao, J. Wu and Z. Zhang, The 2D incompressible Boussinesq equations with general critical dissipation, SIAM J.Math.Anal,46(2014) 3426 –3454.

29. Y. Li, Y. Wu and G. Xu, Low regularity global solutions for the focusing, mass-critical NLS equation in R. SIAM J. Math. Anal., 43:1 (2011), 322-340.

30. C. Miao, X. Tand and G. Xu, Stability of the traveling waves for the derivative Schrodinger equation in the energy space, Calculus of Variations and PDEs, 56(2)(2017), Paper No. 45, 48pp.

31. C. Miao, T. Zhao and J. Zheng, On the 4D Nonlinear Schr\"odinger equation with combined terms under the energy threshold, Calculus of Variations and PDEs (2017) 56:179.

32. C. Miao, J. Zhang and J. Zheng, Strichartz estimates for wave equation with inverse square potential, Contemp. Math., Vol. 15, No. 6 (2013) 1350026 (29 pages).

亿博下载地址 33. D. Li, C. Miao and L. Xue, 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).

亿博下载地址 34. C. Miao and J. Zheng, Scattering theory for NLS below energy space in dimension two, Comm. Contemp. Math., Vol. 17, No. 6 (2015) 1450052 (37 pages).

亿博下载地址 35. D. Li, C. Miao and X. Zhang, On the isentropic compressible Euler equations with adiabatic index $\gamma=1$, Pacific J. Math., 262:1(2013), 109-128.

亿博下载地址 36. C. Miao, J. Zhang and J. Zheng, Maximal estimates for Schrodinger equation with inverse-square potential, Pacific Journal of mathematics,273(2015)1-20.

亿博下载地址 37. Q. Chen, C. Miao and Z. Zhang, Global well-posedness for the 3D rotating Navier-Stokes equations with highly oscillating initial data, Pacific J. Math., 262:2(2013), 263-283.

38. C. Miao, Y. Wu and G. Xu, Dynamics for the focusing, energy-critical nonlinear Hartree equation, Forum Mathematicum. 27, No. 2(2015), 373–447.

亿博下载地址 39. C. Miao, J. Yang and J. Zheng, On Wolff’s L2-Kakeya maximal inequality in R3, Forum Math. 27, No5(2015), 3035-3047.

40. C. Miao, J. Zhang and J. Zheng, Sacttering theory for the radial H1/2-critical wave equation with a cubic convolution, J. Diff. Equat. 259 (2015), 7199–7237.

41. C. Miao and J. Zheng, Energy scattering for a Klein-Gordon Equation with a cubic convolution, J. Diff. Equat.,257(2014), 2178-2224.

42. C. Miao and L. Xue, Global well-posedness for a modified critical dissipative quasi-geostrophic equation,J. Diff. Equat., 252 (2012), 792 - 818.

亿博下载地址 43. Q. Chen and C. Miao,Global well-posedness for the micropolar fluid system in critical Besov spaces,J. Diff. Equat., 252(2012), 2698 - 2724.

44. C. Miao, J. Zhang and J. Zheng, A note on the cone restriction conjecture,Proc. AMS, 140(2012), 2091 - 2102.

45. C. Miao and J. Zhang, On global solution to the Klein–Gordon–Hartree equation below energy space, J. Diff. Equat., 250 (2011), 3418 - 3447.

亿博下载地址 46. C. Miao, Y. Wu and G. Xu, Global well-posedness for Schrodinger equation with derivative in H1/2 (R), J. Diff. Equat., 251 (2011), 2164 - 2195.

47. C. Miao and L. Xue, On the regularity of a class of generalized quasi- geostrophic equations, J. Diff. Equat., 251(2011), 2789-2821.

48. C. Miao, G. Xu and L. Zhao, Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrodinger equations of fourth order in dimensions $d\geq 9$, J. Diff. Equat., 251 (2011), 3381-3402.

49. D. Li, C. Miao and X. Zhang, The focusing energy-critical Hartree equation, J. Diff. Equat., 246 (2009), 1139-1163.

50. C. Miao, G. Xu and L. Zhao, Global wellposedness and scattering for the focusing energy-critical nonlinear Schrodinger equations of fourth order in the radial case, J. Diff. Equat., 246 (2009), 3715–3749.

51. C. Miao and G. Wu, Global well-posedness of the critical Burgers equation in critical Besov spaces, J. Diff. Equat., 247(2009), 1673 --1693.

52. Y. Li, Y. Wu and G. Xu, Global well-posedness for periodic mass-critical nonlinear Schrodinger equation, J. Diff. Equat., 250:6, 15(2011), 2715-2736.

53. X. Tang and G. Xu, Stability of the sum of two solitary waves for (gDNLS) in the energy space, Accepted by J. Diff. Equat.

亿博下载地址 54. W. Chen, J. Li, C. Miao and J. Wu, Low regularity solutions of two fifth-order KdV type equations, Journal D’Analyse Mathematique, 107 (2009), 221-238.

55. W. Chen, C. Miao and J. Li, On the low regularity of the fifth order Kadomtsev–Petviashvili I equation, J. Diff. Equat., 245(2008), 3433 - 3469.

56. Q. Chen and C. Miao, Existence theorem and blow-up criterion of smooth solutions to the two-fluid MHD equations in R3, J. Diff. Equat., 239 (2007), 251 - 271.

57. C. Miao and G. Xu, Global solutions of the Klein-Gordon-Schrodinger system with rough data in R2+1, J. Diff. Equat., 227(2006), 365–405.

58. W. Chen, Y. Han and C. Miao, Factorization theorem for product Hardy spaces. Studia Mathematica, 177(2006), 255-249.

59. C. Miao and J. Zheng, Scattering theory for the defocusing fourth-order Schrodinger Equations, Nonlinearity 29 (2016), 692–736.

亿博下载地址 60. C. Miao, J. Yang and J. Zheng, An improved maximal inequality for 2D fractional order Schr\"{o}dinger operators, Studia Mathematica, 230 (2015), 121-165.

61. C. Miao, J. Yang and J. Zheng, On local smoothing problems and Stein's maximal spherical means, Proc. of AMS, 145 (2017), 4269–4282).

62. X. Cheng, C. Miao and L. Zhao, Global well-posedness and scattering for nonlinear Schrodinger equations with combined nonlinearities, J. Diff. Equat. 261(2016), 2881-2934 .

亿博下载地址 63. C. Miao and Y. Wang, Regularity conditions for the suitable weak solutions of the Navier Stokes system from its rotation form, Pacific J. Math. 288(2017), 189-216.

64. Q. Chen, C. Miao and Z. Zhang, The two-dimensional Euler equations in Yudovich type space and bmo-type space, To appear in Revista Matemtica Iberoamericana, (2017).

亿博下载地址 65. C. Miao, X. Tang and G. Xu, Solitary waves for nonlinear Schrodinger equation with Derivative, Comm. Contemp. Math., (2017), doi: 10.1142 /S0219199717500493, 27pp.

亿博下载地址 66. J. Lu, C. Miao and J. Murphy, Scattering in $H^1$ for the intercritical NLS with an inverse-square potential, J. Diff. Equat., doi:10.1016/j.jde.2017.11.015(2018).

67. D. Li, G. Xu and X. Zhang, On the dispersive estimate for the Dirichlet Schrodinger propagator and applications to energy critical NLS, Canad. J. Math., 66(2014), 1110-1142.

亿博下载地址 68. Q.Chen,and Z.Zhang,Regularity criterion via two components of vorticity on weak solutions to the Navier–Stokes equations in R^3, J.of Differ.Equat.216 (2005) 470-481.

69. Q.Chen, Z.Zhang, Regularity Criterion via the Pressure on Weak Solutions to the 3D Navier-Stokes Equations, Proc. of Amer. Math. Soc. , 135(2007):1829-1837.