非线性偏微分方程，可压缩Navier-Stokes方程

   

070101-基础数学

偏微分方程
可压缩Navier-Stokes方程

   

现代偏微分方程I、II

   

（1） 世界华人数学家联盟五年最佳论文, 二等奖, 其他, 2020
（2） 首届世界华人数学家联盟年会（ICCM）“五年最佳银奖论文”, 二等奖, 其他, 2017

   

[1] Huang, Xiangdi, Meng, Weili, Ni, Anchun. Free boundary value problem for the radial symmetric compressible isentropic Navier-Stokes equations with density-dependent viscosity. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS[J]. 2025, 第 1 作者  通讯作者  548(1): http://dx.doi.org/10.1016/j.jmaa.2025.129377.
[2] Fan, Jie, Gu, Yongteng, Huang, Xiangdi. GLOBAL LARGE STRONG SOLUTION TO THE 3D INCOMPRESSIBLE MHD SYSTEM WITH DENSITY-DEPENDENT VISCOSITY. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS[J]. 2025, 第 3 作者  通讯作者  null(null): http://dx.doi.org/10.3934/dcds.2024178.
[3] Huang, Xiangdi, Xin, Zhouping, Yan, Wei. Finite time blowup of strong solutions to the two dimensional MHD equations. Mathematische Annalen[J]. 2025, 第 1 作者null(null): 1-30, https://link.springer.com/article/10.1007/s00208-025-03148-z.
[4] 段琴, 黄祥娣. Local weak solution of the isentropic compressible Navier-Stokes equations with variable viscosity. Journal of Mathematical Fluid Mechanics[J]. 2024, 第 2 作者26(45): 
[5] 黄祥娣, Menglun Su, 闫伟, 于荣峰. Global large strong solutions to the radially symmetric compressible Navier-Stokes equations in 2D solid balls. Journal of Differential Equations[J]. 2024, 第 1 作者396: 393-429, 
[6] 黄祥娣, 辛周平, 闫伟. 可压缩Navier-Stokes方程无滑移边值问题的高正则整体弱解. 中国科学：数学[J]. 2024, 第 1 作者54(12): 1979-2008, http://lib.cqvip.com/Qikan/Article/Detail?id=7113363600.
[7] 黄祥娣, 李竞. Global well-posedness of classical solutions to the cauchy problem of two-dimensional barotropic compressible Navier-Stokes system with vacuum and large initial data. SIAM J. MATH. ANAL.[J]. 2022, 第 1 作者54(3): 3192-3214, 
[8] 黄祥娣, 段琴. Local weak solutions of the isentropic compressible Navier-Stokes equations in a half-space. Science. China Math[J]. 2022, 第 1 作者65(5): 993-1002, 
[9] Huang, Xiangdi. On local strong and classical solutions to the three-dimensional barotropic compressible Navier-Stokes equations with vacuum. SCIENCE CHINA-MATHEMATICS[J]. 2021, 第 1 作者  通讯作者  64(8): 1771-1788, https://www.webofscience.com/wos/woscc/full-record/WOS:000520050600001.
[10] 黄祥娣, 闫伟. Local weak solutions of the isentropic compressible Navier-Stokes equations. J. Math. Phys[J]. 2021, 第 1 作者  通讯作者  62: 
[11] Wang, Yun, Huang, Xiangdi. On center singularity for compressible spherically symmetric nematic liquid crystal flows. JOURNAL OF DIFFERENTIAL EQUATIONS[J]. 2018, 第 2 作者264(8): 5197-5220, http://dx.doi.org/10.1016/j.jde.2017.12.035.
[12] Huang Xiangdi, 李竞. Global well-posedness of classical solutions to the three-dimensional full compressible Navier-Stokes system with vacuum. Arch. Ration. Mech. Anal.[J]. 2018, 第 1 作者3(227): 995-1059, 
[13] Huang, Xiangdi. A representation formula of incompressible liquid crystal flow and its applications. NONLINEARITY[J]. 2017, 第 1 作者  通讯作者  30(5): https://www.webofscience.com/wos/woscc/full-record/WOS:000398308100002.
[14] Huang, Xiangdi. Existence and uniqueness of weak solutions of the compressible spherically symmetric Navier-Stokes equations. JOURNAL OF DIFFERENTIAL EQUATIONS[J]. 2017, 第 1 作者262(3): 1341-1358, http://dx.doi.org/10.1016/j.jde.2016.10.013.
[15] 黄祥娣, 王云. Linfinity continuation principle to the non-barotropic non-resistive magneto-hydrodynamic equations without heat conductivity.. Mathematical Methods in the Applied Sciences[J]. 2016, 第 1 作者4(39): 4234-4245, 
[16] 黄祥娣, 李竞. Existence and blowup behavior of global strong solutions to the two-dimensional barotropic compressible Navier-Stokes system with vacuum and large initial data. J. Math. Pures Appl.[J]. 2016, 第 1 作者1(106): 123-154, 
[17] Huang, Xiangdi, Xin, Zhouping. ON FORMATION OF SINGULARITY FOR NON-ISENTROPIC NAVIER-STOKES EQUATIONS WITHOUT HEAT-CONDUCTIVITY. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS[J]. 2016, 第 1 作者36(8): 4477-4493, http://dx.doi.org/10.3934/dcds.2016.36.4477.
[18] Huang, Xiangdi. On formation of singularity of spherically symmetric nonbarotropic flows. KYOTO JOURNAL OF MATHEMATICS[J]. 2015, 第 1 作者  通讯作者  55(1): 1-15, https://www.webofscience.com/wos/woscc/full-record/WOS:000352114900001.
[19] Huang, Xiangdi, Matsumura, Akitaka. A CHARACTERIZATION ON BREAKDOWN OF SMOOTH SPHERICALLY SYMMETRIC SOLUTIONS OF THE ISENTROPIC SYSTEM OF COMPRESSIBLE NAVIER-STOKES EQUATIONS. OSAKA JOURNAL OF MATHEMATICS[J]. 2015, 第 1 作者  通讯作者  52(1): 271-283, https://www.webofscience.com/wos/woscc/full-record/WOS:000350943500014.
[20] Huang, Xiangdi, Wang, Yun. Global strong solution of 3D inhomogeneous Navier-Stokes equations with density-dependent viscosity. JOURNAL OF DIFFERENTIAL EQUATIONS[J]. 2015, 第 1 作者259(4): 1606-1627, http://dx.doi.org/10.1016/j.jde.2015.03.008.
[21] Huang, Xiangdi, Wang, Yun. GLOBAL STRONG SOLUTION WITH VACUUM TO THE TWO DIMENSIONAL DENSITY-DEPENDENT NAVIER-STOKES SYSTEM. SIAM JOURNAL ON MATHEMATICAL ANALYSIS[J]. 2014, 第 1 作者  通讯作者  46(3): 1771-1788, https://www.webofscience.com/wos/woscc/full-record/WOS:000338830800003.
[22] He, Cheng, Huang, Xiangdi, Wang, Yun. On some new global existence results for 3D magnetohydrodynamic equations. NONLINEARITY[J]. 2014, 第 2 作者27(2): 343-352, https://www.webofscience.com/wos/woscc/full-record/WOS:000331624600009.
[23] Huang, Xiangdi, Li, Jing. Serrin-Type Blowup Criterion for Viscous, Compressible, and Heat Conducting Navier-Stokes and Magnetohydrodynamic Flows. COMMUNICATIONS IN MATHEMATICAL PHYSICS[J]. 2013, 第 1 作者  通讯作者  324(1): 147-171, https://www.webofscience.com/wos/woscc/full-record/WOS:000325626900007.
[24] Huang, Xiangdi, Li, Jing, Wang, Yong. Serrin-Type Blowup Criterion for Full Compressible Navier-Stokes System. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS[J]. 2013, 第 1 作者  通讯作者  207(1): 303-316, https://www.webofscience.com/wos/woscc/full-record/WOS:000313069100009.
[25] Huang, Xiangdi, Wang, Yun. Global strong solution to the 2D nonhomogeneous incompressible MHD system. JOURNAL OF DIFFERENTIAL EQUATIONS[J]. 2013, 第 1 作者254(2): 511-527, http://dx.doi.org/10.1016/j.jde.2012.08.029.
[26] Craig, Walter, Huang, Xiangdi, Wang, Yun. Global Wellposedness for the 3D Inhomogeneous Incompressible Navier-Stokes Equations. JOURNAL OF MATHEMATICAL FLUID MECHANICS[J]. 2013, 第 2 作者15(4): 747-758, https://www.webofscience.com/wos/woscc/full-record/WOS:000326933000006.
[27] Huang, Xiangdi, Wang, Yun. A Serrin criterion for compressible nematic liquid crystal flows. MATHEMATICAL METHODS IN THE APPLIED SCIENCES[J]. 2013, 第 1 作者36(11): 1363-1375, https://www.webofscience.com/wos/woscc/full-record/WOS:000320783200006.
[28] Bresch, Didier, Huang, Xiangdi, Li, Jing. Global Weak Solutions to One-Dimensional Non-Conservative Viscous Compressible Two-Phase System. COMMUNICATIONS IN MATHEMATICAL PHYSICS[J]. 2012, 第 2 作者309(3): 737-755, http://dx.doi.org/10.1007/s00220-011-1379-6.
[29] Huang, Xiangdi, Li, Jing, Xin, Zhouping. Global well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier-Stokes equations. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS[J]. 2012, 第 1 作者  通讯作者  65(4): 549-585, http://dx.doi.org/10.1002/cpa.21382.
[30] Huang, Xiangdi, Li, Jing, Xin, Zhouping. Blowup Criterion for Viscous Baratropic Flows with Vacuum States. COMMUNICATIONS IN MATHEMATICAL PHYSICS[J]. 2011, 第 1 作者  通讯作者  301(1): 23-35, http://dx.doi.org/10.1007/s00220-010-1148-y.
[31] Bresch, D, Huang, X. A Multi-Fluid Compressible System as the Limit of Weak Solutions of the Isentropic Compressible Navier-Stokes Equations. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS[J]. 2011, 201(2): 647-680, https://www.webofscience.com/wos/woscc/full-record/WOS:000292970700008.
[32] Huang, Xiangdi, Li, Jing, Xin, Zhouping. SERRIN-TYPE CRITERION FOR THE THREE-DIMENSIONAL VISCOUS COMPRESSIBLE FLOWS. SIAM JOURNAL ON MATHEMATICAL ANALYSIS[J]. 2011, 第 1 作者  通讯作者  43(4): 1872-1886, http://dx.doi.org/10.1137/100814639.
[33] XiangDi HUANG, ZhouPing XIN. A blow-up criterion for classical solutions to the compressible Navier-Stokes equations. SCIENCE CHINA Mathematics[J]. 2010, 第 1 作者53(3): 671-686, https://www.sciengine.com/doi/10.1007/s11425-010-0042-6.
[34] 黄祥娣. On breakdown of solutions to the full compressible Navier-Stokes equations. Methods and applications of analysis[J]. 2009, 第 1 作者4(16): 479-490, 
[35] 黄祥娣. A blowup criterion for the full compressible Navier-Stokes equations. Methods and applications of analysis[J]. 2009, 第 1 作者4(16): 491-506, 

   

（ 1 ） 流体力学方程中的大震荡和低正则解, 负责人, 国家任务, 2020-01--2023-12
（ 2 ） 高维激波以及非线性守恒律方程的低正则解, 参与, 国家任务, 2018-01--2022-12
（ 3 ） Navier-Stokes方程组的若干存在性问题, 负责人, 国家任务, 2015-01--2018-12
（ 4 ） 可压缩流体方程组的若干数学理论研究, 参与, 国家任务, 2017-01--2020-12
（ 5 ） 流体力学方程组的数学理论, 参与, 国家任务, 2021-11--2026-11
（ 6 ） Navier-Stokes方程的解, 负责人, 中国科学院计划, 2022-07--2027-07

（1）On existence and blowup behavior of the compressible Navier-Stokes equations and related models: from Nash’s conjecture to front edge   世界华人数学家大会   2022-07-31
（2）Global classical and weak solutions to the three-dimenional full compressible Navier-Stokes system with vacuum and large oscillations   第四届世界华人数学家联盟年会   2020-12-27
（3）Global large solutions of two dimensional compressible Navier–Stokes equations in the whole space   流体力学数学理论国际研讨会   2019-07-04
（4）Global large solutions of two dimensional compressible Navier–Stokes equations in the whole space   2019-06-04
（5）Global large solutions of two dimensional compressible Navier–Stokes equations in the whole space   2019京川偏微分方程学术会议   2019-04-30
（6）Global solvability of full compressible Naiver-Stokes equations   中国工业与应用数学学会第十六届年会   2018-09-13
（7）Global large solutions of two dimensional compressible Navier–Stokes equations in the whole space   流体力学中的偏微分方程国际学术会议   2018-05-25
（8）Global well-posedness of classical solutions with large oscillations and vacuum to the three dimensional isentropic compressible Navier-Stokes equations   2018-03-14
（9）Global well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier-Stokes equations   第一届世界华人数学家联盟年会   2017-12-27