Existence and Regularity of the Pressure for the Stochastic Navier–Stokes Equations

Existence and Regularity of the Pressure for the Stochastic Navier–Stokes Equations We prove, on one hand, that for a convenient body force with values in the distribution space ( H -1 ( D )) d , where D is the geometric domain of the fluid, there exist a velocity u and a pressure p solution of the stochastic Navier–Stokes equation in dimension 2, 3 or 4. On the other hand, we prove that, for a body force with values in the dual space V ’ of the divergence free subspace V of ( H 1 0 ( D )) d , in general it is not possible to solve the stochastic Navier–Stokes equations. More precisely, although such body forces have been considered, there is no topological space in which Navier–Stokes equations could be meaningful for them. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Existence and Regularity of the Pressure for the Stochastic Navier–Stokes Equations

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Publisher
Springer-Verlag
Copyright
Copyright © 2003 by Springer-Verlag
Subject
Philosophy
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-003-0773-7
Publisher site
See Article on Publisher Site

Abstract

We prove, on one hand, that for a convenient body force with values in the distribution space ( H -1 ( D )) d , where D is the geometric domain of the fluid, there exist a velocity u and a pressure p solution of the stochastic Navier–Stokes equation in dimension 2, 3 or 4. On the other hand, we prove that, for a body force with values in the dual space V ’ of the divergence free subspace V of ( H 1 0 ( D )) d , in general it is not possible to solve the stochastic Navier–Stokes equations. More precisely, although such body forces have been considered, there is no topological space in which Navier–Stokes equations could be meaningful for them.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Oct 1, 2003

References

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