On the Well-Posedness of the Dissipative Kadomtsev–Petviashvili Equation

The well-posedness of the initial-value problem associated with the dissipative Kadomtsev–Petviashvili equation in the case of two-dimensional space is studied. It is proved by using a dyadic partition of unity in Fourier variables that the Cauchy problem associated with this equation is globally well posed in the anisotropic Sobolev space $H^{s,0}(\mathbb{R}^2)$ for all $s>-1/2$. It is also shown that this result is sharp in a certain sense.