Approximation of a solution to the Euler equation by solutions of the Navier–Stokes equation

0389760 - MÚ 2013 RIV CH eng J - Článek v odborném periodiku
Neustupa, Jiří - Penel, P.
Approximation of a solution to the Euler equation by solutions of the Navier–Stokes equation.
Journal of Mathematical Fluid Mechanics. Roč. 15, č. 1 (2013), s. 179-196. ISSN 1422-6928. E-ISSN 1422-6952
Grant CEP: GA ČR GA201/08/0012
Institucionální podpora: RVO:67985840
Klíčová slova: Euler equations * Navier-Stokes equations * weak solutions
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 1.305, rok: 2013
http://link.springer.com/article/10.1007%2Fs00021-012-0125-y

We show that a smooth solution u 0 of the Euler boundary value problem on a time interval (0, T 0) can be approximated by a family of solutions of the Navier–Stokes problem in a topology of weak or strong solutions on the same time interval (0, T 0). The solutions of the Navier–Stokes problem satisfy Navier’s boundary condition, which must be “naturally inhomogeneous” if we deal with the strong solutions. We provide information on the rate of convergence of the solutions of the Navier–Stokes problem to the solution of the Euler problem for ν → 0. We also discuss possibilities when Navier’s boundary condition becomes homogeneous.
Trvalý link: http://hdl.handle.net/11104/0218629