A partially strong solution to the steady Navier-Stokes equations for compressible barotropic fluid with generalized impermeability boundary conditions

0349654 - MÚ 2011 RIV GB eng J - Journal Article
Muzereau, O. - Neustupa, Jiří - Penel, P.
A partially strong solution to the steady Navier-Stokes equations for compressible barotropic fluid with generalized impermeability boundary conditions.
Nonlinearity. Roč. 23, č. 12 (2010), s. 3071-3090. ISSN 0951-7715. E-ISSN 1361-6544
R&D Projects: GA ČR GA201/08/0012
Institutional research plan: CEZ:AV0Z10190503
Keywords : Navier-Stokes equations * compressible fluids * weak solution
Subject RIV: BA - General Mathematics
Impact factor: 1.468, year: 2010
http://iopscience.iop.org/0951-7715/23/12/005/

We prove the existence of a partially strong solution to the steady Navier-Stokes equations for barotropic compressible fluid in a bounded simply connected domain with the prescribed generalized impermeability conditions u.n=0, curl u.n=0 and curl curl u.n=0 on the boundary. We assume that the state law for the pressure has the form P(rho)=rho^{gamma} for gamma>3. We call the solution "partially strong" because only the divergence - free part of velocity and the effective pressure have regularity typical for strong solutions, while the gradient part of velocity and the density have regularity typical for weak solutions.
Permanent Link: http://hdl.handle.net/11104/0189833