6533b85efe1ef96bd12bfbca

RESEARCH PRODUCT

Hydrodynamics and Stochastic Differential Equation with Sobolev Coefficients

Shizan Fang

subject

Stochastic partial differential equationSobolev spacesymbols.namesakeStochastic differential equationDifferential equationOrdinary differential equationMathematics::Analysis of PDEssymbolsCharacteristic equationFirst-order partial differential equationApplied mathematicsMathematicsEuler equations

description

In this chapter, we will explain how the Brenier’s relaxed variational principle for Euler equation makes involved the ordinary differential equations with Sobolev coefficients and how the investigation on stochastic differential equations (SDE) with Sobolev coefficients is useful to establish variational principles for Navier–Stokes equations. We will survey recent results on this topic.

yearjournalcountryeditionlanguage
2013-12-28
https://doi.org/10.1007/978-3-319-03512-3_7