Classical solution to a multidimensional stochastic Burgers equation via forward-backward SDEs

2016/02/19 by Alberto Ohashi, Ohashi, Alberto, Evelina Shamarova +1
Economics, Econometrics and Finance · Engineering · Mathematics · #Stochastic processes and financial applications #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1602.06268

Abstract

In this paper, we address the problem of existence and uniqueness of a global classical solution to a multidimensional stochastic Burgers equation without gradient-type assumptions on the force or the initial condition. The equation is first transformed to a random PDE, and then solved via the associated forward-backward SDE. Additionally, we obtain a new a priori gradient estimate valid for a large class of second-order quasilinear parabolic PDEs which becomes an important tool in our approach. Also, we study the stochastic Burgers equation in the vanishing viscosity limit.

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