我们将文献(Cipriano F,Cruzeiro A B.Navier-Stokes equation and diffusions onthe group of homeomorphisms of the Torus[J].Commun.Math.Phys.,2007,275:255-269)推广到三维情形,即给出三维环面上的Navier-Stokes方程的随机变分准则.
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 ...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.展开更多
文摘我们将文献(Cipriano F,Cruzeiro A B.Navier-Stokes equation and diffusions onthe group of homeomorphisms of the Torus[J].Commun.Math.Phys.,2007,275:255-269)推广到三维情形,即给出三维环面上的Navier-Stokes方程的随机变分准则.
基金supported by China Scholarship Council(State Scholarship Fund)
文摘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.
