Existence and uniqueness of global solutions to a model for the flow of an incompressible, barotropic fluid with capillary effects
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...
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| Format: | Article |
| Language: | English |
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Texas State University
2007-03-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2007/39/abstr.html |
| 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 $ ho$, and using the smallness of the initial velocity gradient, to obtain uniqueness for the density. |
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| ISSN: | 1072-6691 |