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A model of stochastic differential equation in Hilbert applicable to Navier-Stokes equation in dimension 2

Alain Bensoussan

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Abstract

Nagase has given new results for the existence of solutions of stochastic partial differential equations. The main idea is to use a compactness argument based on a special Hilbert space introduced by J. L. Lions (1961) in the context of parabolic linear partial differential equations. Previously, the author considered a class of nonlinear partial differential equations which generalize those of Nagase as far as the nonlinearity is considered. Here the author considers another class of nonlinearity which covers the Navier-Stokes equation in dimension 2.>

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What this paper is about

Nagase has given new results for the existence of solutions of stochastic partial differential equations. The main idea is to use a compactness argument based on a special Hilbert space introduced by J. L. Lions (1961) in the context of parabolic linear partial differential equations. Previously, the author considered a class of nonlinear partial differential equations which generalize those of Nagase as far as the nonlinearity is considered. Here the author considers another class of nonlinearity which covers the Navier-Stokes equation in dimension 2.>

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Available abstract

Nagase has given new results for the existence of solutions of stochastic partial differential equations. The main idea is to use a compactness argument based on a special Hilbert space introduced by J. L. Lions (1961) in the context of parabolic linear partial differential equations. Previously, the author considered a class of nonlinear partial differential equations which generalize those of Nagase as far as the nonlinearity is considered. Here the author considers another class of nonlinearity which covers the Navier-Stokes equation in dimension 2.>

Key concepts: Mathematics, Partial differential equation, Hilbert space, Stochastic partial differential equation, Nonlinear system, Dimension (graph theory), Context (archaeology), Mathematical analysis

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