Nikolai Larkin
Published 2014-08-25Version 1
An initial-boundary value problem for the 2D Kawahara-Burgers equation posed on a channel-type strip was considered. The existence and uniqueness results for regular and weak solutions in weighted spaces as well as exponential decay of small solutions without restrictions on the width of a strip were proven both for regular solutions in an elevated norm and for weak solutions in the $L^2$-norm.
Comments: There are not published results on the existence and decay properties for global regular and weak solutions for the 2D Kawahara-Burgers equation posed on a strip. This seemed to me interesting and challenging. arXiv admin note: substantial text overlap with arXiv:1404.4638
The 2D Zakharov-Kuznetsov-Burgers equation on a strip
The Navier-Stokes Equations with the Kinematic and Vorticity Boundary Conditions on Non-Flat Boundaries
Spatial analyticity and exponential decay of Fourier modes for the stochastic Navier-Stokes equation
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