On the motion of incompressible inhomogeneous Euler-Kortewegfluids

Miroslav Bulíček; Eduard Feireisl; Josef Málek; Roman Shvydkoy

doi:10.3934/dcdss.2010.3.497

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2010, Volume 3, Issue 3: 497-515. Doi: 10.3934/dcdss.2010.3.497

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On the motion of incompressible inhomogeneous Euler-Korteweg fluids

1.
Mathematical Institute of Charles University, Sokolovská 83, 186 75 Prague
2.
Institute of Mathematics AS ČR, Žitná 25, 115 67 Praha 1
3.
Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 S. Morgan St. M/C 249 Chicago, IL 60607-7045

Received: March 2010

Revised: April 2010

Published: September 2010

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Abstract

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 $\frac{n}{2}+1$.

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Mathematics Subject Classification: 76A05, 35A01.

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