Global solutions for the Kuramoto-Sivashinsky equation posed on unbounded 3D grooves
Nikolai Larkin
TL;DR
This paper proves the existence, uniqueness, and exponential decay of global strong solutions for the 3D Kuramoto-Sivashinsky equation on unbounded grooves, advancing understanding of complex PDE behavior in unbounded domains.
Contribution
It establishes the first rigorous results on global solutions and their decay for the 3D Kuramoto-Sivashinsky equation in unbounded geometries.
Findings
Existence of global strong solutions
Uniqueness of solutions
Exponential decay of solutions
Abstract
Initial boundary value problems for the three dimensional Kuramoto-Sivashinsky equation posed on unbounded 3D grooves were considered. The existence and uniqueness of global strong solutions as well as their exponential decay have been established.
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