# American Institute of Mathematical Sciences

June  2004, 3(2): 197-216. doi: 10.3934/cpaa.2004.3.197

## Existence of solutions to equations for the flow of an incompressible fluid with capillary effects

 1 Department of Mathematics, University of Wyoming, Laramie, Wyoming 82071, United States

Received  March 2003 Revised  November 2003 Published  March 2004

We study the initial-value problem for a system of equations that models the low-speed flow of an inviscid, incompressible fluid with capillary stress effects. The system includes hyperbolic equations for the density and velocity, and an algebraic equation (the equation of state). We prove the local existence of a unique, classical solution to an initial-value problem with suitable initial data. We also derive a new, a priori estimate for the density, and then use this estimate to show that, if the regularity of the initial data for the velocity alone is increased, then the regularity of the solution for the density and the velocity may be increased, by a bootstrapping argument.
Citation: D. L. Denny. Existence of solutions to equations for the flow of an incompressible fluid with capillary effects. Communications on Pure & Applied Analysis, 2004, 3 (2) : 197-216. doi: 10.3934/cpaa.2004.3.197
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