A contribution to the theory of regularity of a weak solution to the Navier-Stokes equations via one component of velocity and other related quantities

0492100 - MÚ 2019 RIV CH eng J - Journal Article
Neustupa, Jiří
A contribution to the theory of regularity of a weak solution to the Navier-Stokes equations via one component of velocity and other related quantities.
Journal of Mathematical Fluid Mechanics. Roč. 20, č. 3 (2018), s. 1249-1267. ISSN 1422-6928. E-ISSN 1422-6952
R&D Projects: GA ČR(CZ) GA17-01747S
Institutional support: RVO:67985840
Keywords : Navier–Stokes equations * weak solution * regularity
OECD category: Pure mathematics
Impact factor: 1.532, year: 2018
https://link.springer.com/article/10.1007%2Fs00021-018-0365-6

We deal with a suitable weak solution (v, p) to the Navier–Stokes equations in (0, T), where is a domain in R3, T > 0 and v = (v1, v2, v3). We show that the regularity of (v, p)at a point (x0, t0) 2 (0, T) is essentially determined by the Serrin–type integrability of the positive part of a certain linear combination of v2 1, v2 2, v2 3 and p in a backward neighborhood of (x0, t0). An appropriate choice of coefficients in the linear combination leads to the Serrin–type condition on one component of v or, alternatively, on the positive part of the Bernoulli pressure 1 2 jvj2 + p or the negative part of p, etc.
Permanent Link: http://hdl.handle.net/11104/0285662