Existence and uniqueness of global solutions to a model for the flow of an incompressible, barotropic fluid with capillary effects
Texas State University-San Marcos, Department of Mathematics
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.
Existence, Uniqueness, Capillary, Incompressible, Inviscid fluid
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.