Abstract:
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.
