Existence of mild solutions for the Hamilton-Jacobi equation with critical fractional viscosity in the Besov spaces

Tsukasa Iwabuchi, Tatsuki Kawakami

We consider the Cauchy problem for the Hamilton-Jacobi equation with critical dissipation, $$ \partial_t u + (-Δ)^{ 1/2} u = |\nabla u|^p, \quad x \in \mathbb R^N, t > 0, \qquad u(…