On space-time properties of solutions for nonlinear evolutionary equations with random initial data - Vaninsky, Kyrill I. (1996)
We consider space-time properties of periodic solutions of nonlinear wave equations, nonlinear Schrödinger equations and KdV-type equations with initial data from the support of the Gibbs’ measure. For the wave and Schrödinger equations we establish the best Hölder exponents. We also discuss KdV-type equations which are more difficult due to a presence of the derivative in the nonlinearity.