Probabilistic global well-posedness to the nonlocal Degasperis–Procesi equation

Abstract

We study the almost sure existence of a global solution of the nonlocal Degasperis–Procesi equation. After a suitable randomization, we obtain the local existence and uniqueness of the mild solution for a large set of the supercritical initial data. Then, we establish an energy estimate of the solution and get the global existence in probability. The methods can be used to get the well-posedness of fractional Burgers equation with the supercritical initial data.