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)
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__a295,
     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},
     year = {2007},
     volume = {2007},
     zbl = {1112.35003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a295/}
}
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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
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VL  - 2007
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%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
%U http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a295/
%G en
%F EJDE_2007__2007__a295
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__a295/