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:2017-04-01
Journal:SCIENCE CHINA-MATHEMATICS
Included Journals:SCIE、Scopus
Volume:60
Issue:4
Page Number:637-650
ISSN No.:1674-7283
Key Words:Navier-Stokes equations; interior regularity criterion; BMO space; Besov space
Abstract:Let u = (u (h), u (3)) be a smooth solution of the 3-D Navier-Stokes equations in a"e(3) x [0, T). It was proved that if u (3) a L (a)(0, T; (B)over dot, (p,q) (-1+3/p) (a"e(3))) for 3 < p,q < a and u (h) a L (a)(0, T; BMO-1(a"e(3))) with u (h)(T) a VMO-1(a"e(3)), then u can be extended beyond T. This result generalizes the recent result proved by Gallagher et al. (2016), which requires u a L (a)(0, T; (B)over dot, (p,q) (-1+3/p) (a"e(3))). Our proof is based on a new interior regularity criterion in terms of one velocity component, which is independent of interest.
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
