On robustness of a strong solution to the Navier–Stokes equations with Navier's boundary conditions in the L3-norm

0473686 - MÚ 2018 RIV GB eng J - Journal Article
Kučera, P. - Neustupa, Jiří
On robustness of a strong solution to the Navier–Stokes equations with Navier's boundary conditions in the L3-norm.
Nonlinearity. Roč. 30, č. 4 (2017), s. 1564-1583. ISSN 0951-7715. E-ISSN 1361-6544
R&D Projects: GA ČR GA13-00522S
Institutional support: RVO:67985840
Keywords : Navier-Stokes equations * slip boundary conditions * regularity
OECD category: Pure mathematics
Impact factor: 1.926, year: 2017
http://iopscience.iop.org/article/10.1088/1361-6544/aa6166/meta

We recall or prove a series of results on solutions to the Navier-Stokes equation with Navier's slip boundary conditions. The main theorem says that a strong solution u on any time interval (0,T) (where ...) is robust in the sense that small perturbations of the initial value in the norm of L^3(Omega) and the acting body force in the norm of L^2(0,T:, L^{3/2}(Omega)) cause only a small perturbation of solution u in the norm of L^3(Omega). This result particularly implies that the maximum length of the time interval, on which the solution starting from the initial value u_0 in L^3(Omega) is regular, is a lower semi-continuous functional on L^3(Omega).
Permanent Link: http://hdl.handle.net/11104/0270813