On a nu-continuous famaly of strong solutions to the Euler or Navier-Stokes equations with the Navier-type boundary condition

0343551 - MÚ 2011 RIV US eng J - Journal Article
Bellout, H. - Neustupa, Jiří - Penel, P.
On a nu-continuous famaly of strong solutions to the Euler or Navier-Stokes equations with the Navier-type boundary condition.
Discrete and Continuous Dynamical Systems. Roč. 27, č. 4 (2010), s. 1353-1373. ISSN 1078-0947. E-ISSN 1553-5231
R&D Projects: GA AV ČR IAA100190905
Institutional research plan: CEZ:AV0Z10190503
Keywords : Euler equations * Navier-Stokes equations * zero viscosity limit
Subject RIV: BA - General Mathematics
Impact factor: 0.986, year: 2010
http://www.aimsciences.org/journals/displayArticles.jsp?paperID=5028

Under assumptions on smoothness of the initial velocity and the external body force, we prove that there exists T-0 > 0, nu* > 0 and a unique family of strong solutions u(nu) of the Euler or Navier-Stokes initial-boundary value problem on the time interval ( 0, T-0), depending continuously on the viscosity coefficient nu for 0 <= nu < nu*. The solutions of the Navier-Stokes problem satisfy a Navier-type boundary condition. We give the information on the rate of convergence of the solutions of the Navier-Stokes problem to the solution of the Euler problem for nu -> 0+.
Permanent Link: http://hdl.handle.net/11104/0186002