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arXiv · 2103.02971

Global Existence for the Two-dimensional Kuramoto-Sivashinsky equation with a Shear Flow

Michele Coti Zelati·Michele Dolce·Yuanyuan Feng·Anna L. Mazzucato
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Abstract

We consider the Kuramoto-Sivashinsky equation (KSE) on the two-dimensional torus in the presence of advection by a given background shear flow. Under the assumption that the shear has a finite number of critical points and there are linearly growing modes only in the direction of the shear, we prove global existence of solutions with data in $L^2$, using a bootstrap argument. The initial data can be taken arbitrarily large.

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Michele Coti Zelati, Michele Dolce, Yuanyuan Feng, Anna L. Mazzucato. 2021-03-04. Global Existence for the Two-dimensional Kuramoto-Sivashinsky equation with a Shear Flow. https://arxiv.org/abs/2103.02971

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