Geodesic
Existence and uniqueness of global solutions to a model for the flow of an incompressible, barotropic fluid with capillary effects
Electronic Journal of Differential Equations, Tome 2007 (2007).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study the initial-value problem for a system of nonlinear equations that models the flow of an inviscid, incompressible, barotropic fluid with capillary stress effects. We prove the global-in-time existence of a unique, classical solution to this system of equations, with a small initial velocity gradient. The key to the proof lies in using an $L^2$ estimate for the density $\rho$, and using the smallness of the initial velocity gradient, to obtain uniqueness for the density.
Classification : 35A05
Keywords: existence, uniqueness, capillary, incompressible, inviscid fluid 
@article{EJDE_2007__2007__a195,
     author = {Denny, Diane L.},
     title = {Existence and uniqueness of global solutions to a model for the flow of an incompressible, barotropic fluid with capillary effects},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2007},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a195/}
}
TY  - JOUR
AU  - Denny, Diane L.
TI  - Existence and uniqueness of global solutions to a model for the flow of an incompressible, barotropic fluid with capillary effects
JO  - Electronic Journal of Differential Equations
PY  - 2007
VL  - 2007
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a195/
LA  - en
ID  - EJDE_2007__2007__a195
ER  - 
%0 Journal Article
%A Denny, Diane L.
%T Existence and uniqueness of global solutions to a model for the flow of an incompressible, barotropic fluid with capillary effects
%J Electronic Journal of Differential Equations
%D 2007
%V 2007
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a195/
%G en
%F EJDE_2007__2007__a195
Denny, Diane L. Existence and uniqueness of global solutions to a model for the flow of an incompressible, barotropic fluid with capillary effects. Electronic Journal of Differential Equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a195/