American Institute of Mathematical Sciences

Advanced
2010, 3(3): 497-515. doi: 10.3934/dcdss.2010.3.497

On the motion of incompressible inhomogeneous Euler-Korteweg fluids

Miroslav Bulíček 1, , Eduard Feireisl 2, , Josef Málek 1, and  Roman Shvydkoy 3,

1. 

Mathematical Institute of Charles University, Sokolovská 83, 186 75 Prague, Czech Republic, Czech Republic
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  May 2010

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 $\frac{n}{2}+1$.
Keywords: local-in-time well-posedness, smooth solution., Korteweg stress, Korteweg fluid, inhomogeneous Euler fluid.
Mathematics Subject Classification: 76A05, 35A0.
Citation: Miroslav Bulíček, Eduard Feireisl, Josef Málek, Roman Shvydkoy. On the motion of incompressible inhomogeneous Euler-Korteweg fluids. Discrete & Continuous Dynamical Systems - S, 2010, 3 (3) : 497-515. doi: 10.3934/dcdss.2010.3.497
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