On the well-posedness of the anisotropically-reduced two-dimensional Kuramoto-Sivashinsky Equation

David Massatt

doi:10.3934/dcdsb.2021305

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2022, Volume 27, Issue 10: 6023-6036. Doi: 10.3934/dcdsb.2021305

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On the well-posedness of the anisotropically-reduced two-dimensional Kuramoto-Sivashinsky Equation

David Massatt

Department of Mathematics, University of Southern California, Los Angeles, CA, 90089, USA

Received: February 2021

Revised: October 2021

Published: October 2022

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Abstract

We address the global existence and uniqueness of solutions for the anisotropically reduced 2D Kuramoto-Sivashinsky equations in a periodic domain with initial data $ u_{01} \in L^2 $ and $ u_{02} \in H^{-1 + \eta} $ for $ \eta > 0 $.

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Mathematics Subject Classification: Primary: 35K25, 35A01.

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