The interior regularity of pressure associated with a weak solution to the Navier-Stokes equations with the Navier-type boundary conditions

0489052 - MÚ 2019 RIV US eng J - Journal Article
Neustupa, Jiří - Al Baba, Hind
The interior regularity of pressure associated with a weak solution to the Navier-Stokes equations with the Navier-type boundary conditions.
Journal of Mathematical Analysis and Applications. Roč. 463, č. 1 (2018), s. 222-234. ISSN 0022-247X. E-ISSN 1096-0813
R&D Projects: GA ČR(CZ) GA17-01747S
Institutional support: RVO:67985840
Keywords : Navier-Stokes equation * Navier-type boundary conditions * interior regularity
OECD category: Pure mathematics
Impact factor: 1.188, year: 2018
https://www.sciencedirect.com/science/article/pii/S0022247X18302233?via%3Dihub

We prove that if u is a weak solution to the Navier-Stokes system with the Navier-type boundary conditions in Omega x (0,T), satisfying the strong energy inequality in Omega x (0,T) and Serrin's integrability conditions in Omega' x (t1,t2) (where Omega' is a sub-domain of Omega and 0<= t1<t2<=T) then p and the time-derivative of u have spatial derivatives of all orders essentially bounded in Omega'' x (t1+e,t2-e) for any bounded sub-domain Omega'' of Omega' and e>0 so small that t1+e<t2-e. (See Theorem 1.) We show an application of Theorem 1 to the procedure of localization.
Permanent Link: http://hdl.handle.net/11104/0283538