A Stochastic Variational Approach to Viscous Burgers Equations
A Stochastic Variational Approach to Viscous Burgers Equations
摘要
We consider viscous Burgers equations in one dimension of space and derive their solutions from stochastic variational principles on the corresponding group of homeomorphisms. The metrics considered on this group are Lp metrics. The velocity corresponds to the drift of some stochastic Lagrangian processes. Existence of minima is proved in some cases by direct methods. We also give a representation of the solutions of viscous Burgers equations in terms of stochastic forward-backward systems.
We consider viscous Burgers equations in one dimension of space and derive their solutions from stochastic variational principles on the corresponding group of homeomorphisms. The metrics considered on this group are Lp metrics. The velocity corresponds to the drift of some stochastic Lagrangian processes. Existence of minima is proved in some cases by direct methods. We also give a representation of the solutions of viscous Burgers equations in terms of stochastic forward-backward systems.
基金
supported by China Scholarship Council(State Scholarship Fund)
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