Analyticity and Gevrey class regularity for a Kuramoto-Sivashinsky equation in space dimension two (Q5938911)

This paper is devoted to the time analyticity and Gevrey class regularity in the space variable for the following variation of the Kuramoto-Sivashinsky equation NEWLINE\[NEWLINE{\partial u\over\partial t}+ \Delta^2u+ {\partial^2u\over\partial x^2}+ u{\partial u\over\partial x}= 0,NEWLINE\]NEWLINE NEWLINE\[NEWLINEu(t, x+ L,y)= u(t,x,y+ L)= u(t,x,y),\quad u(0,x,y)= u_0(x,y).NEWLINE\]NEWLINE The proof is based on a well-known result of Foias and Temam on Navier-Stokes equations with periodic boundary conditions.