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
Hits:
Indexed by:期刊论文
Date of Publication:2015-01-01
Journal:JOURNAL OF DIFFERENTIAL EQUATIONS
Included Journals:SCIE
Volume:258
Issue:1
Page Number:224-241
ISSN No.:0022-0396
Key Words:Carleman inequality; Backward uniqueness; Cone domain; Parabolic operator
Abstract:Consider the system vertical bar partial derivative(t)u + Delta u vertical bar <= M(vertical bar u vertical bar+vertical bar del u vertical bar), vertical bar u(x, t)vertical bar <= Me-M vertical bar x vertical bar 2 in C-theta x [0, T] and u(x, 0) = 0 in C-theta, where C-theta is a cone with opening angle theta. L. Escauriaza constructed an example to show that such system has a nonzero solution when theta < 90 degrees, and it's conjectured that the system has only zero solution when theta > 90 degrees. Lu Li and V. Sverak proved that the conjecture is true when theta > 109.5 degrees. Here we improve their result and prove that the conjecture is true when theta > 99 degrees by exploring a new type of Carleman inequality, which is of independent interest. (C) 2014 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
