Existence and uniqueness of global solutions to a model for the flow of an incompressible, barotropic fluid with capillary effects
Date
2007-03-06
Authors
Denny, Diane
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
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 L2 estimate for the density ρ, and using the smallness of the initial velocity gradient, to obtain uniqueness for the density.
Description
Keywords
Existence, Uniqueness, Capillary, Incompressible, Inviscid fluid
Citation
Denny, D. L. (2007). Existence and uniqueness of global solutions to a model for the flow of an incompressible, barotropic fluid with capillary effects. <i>Electronic Journal of Differential Equations, 2007</i>(39), pp. 1-23.