On the motion of incompressible inhomogeneous Euler-Korteweg fluids

0349263 - MÚ 2011 RIV US eng J - Journal Article
Bulíček, M. - Feireisl, Eduard - Málek, J. - Shvydkoy, R.
On the motion of incompressible inhomogeneous Euler-Korteweg fluids.
Discrete and Continuous Dynamical systems - Series S. Roč. 3, č. 3 (2010), s. 497-515. ISSN 1937-1632. E-ISSN 1937-1179
R&D Projects: GA MŠMT LC06052; GA ČR GA201/09/0917
Institutional research plan: CEZ:AV0Z10190503
Keywords : Korteweg fluid * inhomogeneous Euler fluid * Korteweg stress * local-in-time well-posedness * smooth solution
Subject RIV: BA - General Mathematics
http://www.aimsciences.org/journals/displayArticles.jsp?paperID=5226

We study a system of equations governing evolution of incompressible inhomogeneous Euler-Korteweg fluids that describe a class of incompressible elastic materials. A local well-posedness theory is developed on a bounded smooth domain with no-slip boundary condition on velocity and vanishing gradient of density. The cases of open space and periodic box are also considered, where the local existence and uniqueness of solutions is shown in Sobolev spaces up to the critical smoothness n/2+1.
Permanent Link: http://hdl.handle.net/11104/0189550