Global solvability of the Kuramoto-Sivashinsky equation with bounded initial data

The paper considers initial-boundary-value problems for the Kuramoto-Sivashinsky equation both with Dirichlet boundary conditions and with Navier-type boundary conditions when $t>0$ and $x\in\Omega\subset\mathbb R^N$, $N\le3$. Given bounded initial data, the problems in question are shown to be uniquely globally (in $t>0$) solvable in relevant classes of functions.
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