The Inviscid Burgers Equation with Brownian Initial Velocity

Abstract:The law of the (Hopf-Cole) solution of the inviscid Burgers equation with Brownian initial velocity is made explicit. As examples of applications, we investigate the smoothness of the solution, the statistical distribution of the shocks, we determine the exact Hausdorff function of the Lagrangian regular points and investigate the existence of Lagrangian regular points in a fixed Borel set.

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