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

Journal Article · Wed Oct 15 04:00:00 EDT 2003 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-003-0773-7· OSTI ID:21064229

Real, Jose ^[1]; Simon, Jacques ^[2]

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1. Department of Differential Equations and Numerical Analysis, University of Sevilla, Tarfia s/n, E-41012 Sevilla (Spain)
2. Laboratoire de Mathematiques Appliquees, CNRS and Universite Blaise Pascal, 63177 Aubiere cedex (France)

We prove, on one hand, that for a convenient body force with value sin the distribution space (H{sup -1}(D)){sup 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{sup 1}{sub 0}(D)){sup 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.

• OSTI ID: 21064229
• Journal Information: Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 3 Vol. 48; ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DISTRIBUTION
FLUIDS
FOUR-DIMENSIONAL CALCULATIONS
MATHEMATICAL SPACE
NAVIER-STOKES EQUATIONS
STOCHASTIC PROCESSES
THREE-DIMENSIONAL CALCULATIONS
TOPOLOGY
TWO-DIMENSIONAL CALCULATIONS