TY  - JOUR
ID  - ncmm-2009-041
T1  - On the motion of incompressible inhomogeneous Euler-Korteweg fluids
A1  - Bulíček, Miroslav
A1  - Feireisl, Eduard
A1  - Málek, Josef
A1  - Shvydkoy, Roman
JA  - Discrete and Continuous Dynamical Systems - Series S
Y1  - 2010
VL  - 3
IS  - 3
SP  - 497
EP  - 515
N1  - NCMM Preprint no. 2009-041
UR  - http://www.karlin.mff.cuni.cz/ncmm/preprints/09329203040pr41.pdf
M2  - doi: 10.3934/dcdss.2010.3.497
KW  - inhomogeneous Euler fluid
KW  - Korteweg fluid
KW  - Korteweg stress
KW  - local-in-time well-posedness
KW  - smooth solution
N2  - 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 .
ER  -