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

0389760 - MÚ 2013 RIV CH eng J - Journal Article
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
R&D Projects: GA ČR GA201/08/0012
Institutional support: RVO:67985840
Keywords : Euler equations * Navier-Stokes equations * weak solutions
Subject RIV: BA - General Mathematics
Impact factor: 1.305, year: 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.
Permanent Link: http://hdl.handle.net/11104/0218629