研究领域
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
近期论文
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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)
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