Michael
Professor Supervisor of Doctorate Candidates Supervisor of Master's Candidates
Gender:Male
Alma Mater:Chinese Academy of Sciences
Degree:Doctoral Degree
School/Department:School of Mathematical Sciences
Discipline:Pure Mathematics. Applied Mathematics
E-Mail:wendong@dlut.edu.cn
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Indexed by:期刊论文
Date of Publication:2018-02-05
Journal:JOURNAL OF DIFFERENTIAL EQUATIONS
Included Journals:SCIE
Volume:264
Issue:3
Page Number:2351-2376
ISSN No.:0022-0396
Key Words:Navier-Stokes equations; MHD equations; Suitable weak solutions; Boundary regularity
Abstract:It is shown in this paper that suitable weak solutions to the 6D steady incompressible Navier-Stokes and MHD equations are Holder continuous near boundary provided that either
r(-3) integral(+)(Br) vertical bar u(x)vertical bar(3) dx or r(-2) integral(+)(Br) vertical bar del u(x)vertical bar(2) dx is sufficiently small, which implies that the 2D Hausdorff measure of the set of singular points near the boundary is zero. This generalizes recent interior regularity results by Dong-Strain [5]. (c) 2017 Elsevier Inc. All rights reserved.
Tao, Tao; Wang, Wendong; Zhang, Zhifei; Zero-Viscosity Limit of the Navier–Stokes Equations with the Navier Friction Boundary Condition. SIAM J. Math. Anal. 52 (2020), no. 2, 1040–1095.
Seregin, G.; Wang, W. Sufficient conditions on Liouville type theorems for the 3D steady Navier-Stokes equations. Algebra i Analiz 31 (2019), no. 2, 269–278; reprinted in St. Petersburg Math. J. 31 (2020), no. 2, 387–393
Wang, Wendong; Wang, Yuzhao Liouville-type theorems for the stationary MHD equations in 2D. Nonlinearity 32 (2019), no. 11, 4483–4505.
Wang, Wendong Remarks on Liouville type theorems for the 3D steady axially symmetric Navier-Stokes equations. J. Differential Equations 266 (2019), no. 10, 6507–6524.
Liu, Jitao; Wang, Wendong Boundary regularity criteria for the 6D steady Navier-Stokes and MHD equations. J. Differential Equations 264 (2018), no. 3, 2351–2376.
Pu, Xueke; Wang, Meng; Wang, Wendong The Landau-Lifshitz equation of the ferromagnetic spin chain and Oseen-Frank flow. SIAM J. Math. Anal. 49 (2017), no. 6, 5134–5157.
Wang, Meng; Wang, Wendong; Zhang, Zhifei From the Q-tensor flow for the liquid crystal to the harmonic map flow. Arch. Ration. Mech. Anal. 225 (2017), no. 2, 663–683.
Wang, WenDong; Zhang, ZhiFei Blow-up of critical norms for the 3-D Navier-Stokes equations. Sci. China Math. 60 (2017), no. 4, 637–650.
Wang, Wendong; Wei, Dongyi; Zhang, Zhifei Energy identity for approximate harmonic maps from surfaces to general targets. J. Funct. Anal. 272 (2017), no. 2, 776–803.
Wang, Meng; Wang, Wendong; Zhang, Zhifei On the uniqueness of weak solution for the 2-D Ericksen-Leslie system. Discrete Contin. Dyn. Syst. Ser. B 21 (2016), no. 3, 919–941.
Wu, Jie; Wang, Wendong On backward uniqueness for the heat operator in cones. J. Differential Equations 258 (2015), no. 1, 224–241.
Wang, Meng; Wang, Wendong Global existence of weak solution for the 2-D Ericksen-Leslie system. Calc. Var. Partial Differential Equations 51 (2014), no. 3-4, 915–962.
Wang, Wendong; Zhang, Zhifei On the interior regularity criteria and the number of singular points to the Navier-Stokes equations. J. Anal. Math. 123 (2014), 139–170.
Wang, Wendong; Zhang, Zhifei On the interior regularity criteria for suitable weak solutions of the magnetohydrodynamics equations. SIAM J. Math. Anal. 45 (2013), no. 5, 2666–2677.
Wang, Wendong; Zhang, Zhifei Limiting case for the regularity criterion to the 3-D magneto-hydrodynamics equations. J. Differential Equations 252 (2012), no. 10, 5751–5762.
Wang, WenDong; Zhang, LiQun The
