A pressure associated with a weak solution to the Navier-Stokes equations with Navier's boundary conditions

0525121 - MÚ 2021 RIV CH eng J - Journal Article
Neustupa, Jiří - Nečasová, Šárka - Kučera, Petr
A pressure associated with a weak solution to the Navier-Stokes equations with Navier's boundary conditions.
Journal of Mathematical Fluid Mechanics. Roč. 22, č. 3 (2020), č. článku 37. ISSN 1422-6928. E-ISSN 1422-6952
R&D Projects: GA ČR(CZ) GA17-01747S
Institutional support: RVO:67985840
Keywords : Navier-Stokes equations * Navier’s slip boundary conditions * weak solutions * associated pressure
OECD category: Pure mathematics
Impact factor: 1.298, year: 2020
Method of publishing: Limited access
https://doi.org/10.1007/s00021-020-00500-y

We show that if u is a weak solution to the Navier–Stokes initial–boundary value problem with Navier’s slip boundary conditions in QT:=Ω×(0,T), where Ω is a domain in R3, then an associated pressure p exists as a distribution with a certain structure. Furthermore, we also show that if Ω is a “smooth” domain in R3 then the pressure is represented by a function in QT with a certain rate of integrability. Finally, we study the regularity of the pressure in sub-domains of QT, where u satisfies Serrin’s integrability conditions.
Permanent Link: http://hdl.handle.net/11104/0309329