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Well-Posedness of a Model Equation for Water Waves in Fluids with Odd Viscosity
Journal article   Peer reviewed

Well-Posedness of a Model Equation for Water Waves in Fluids with Odd Viscosity

Shunlian Liu and David M. Ambrose
Journal of dynamics and differential equations
08 Apr 2023
DOI: https://doi.org/10.1007/s10884-023-10252-8
Featured in Collection :   UN Sustainable Development Goals @ Drexel

Abstract

Mathematics, Applied Science & Technology Mathematics Physical Sciences
We study an asymptotic model for the motion of capillary-gravity waves in a fluid with non-Newtonian viscosity (known as odd viscosity). This model was one of three which were introduced recently by Granero-Belinchon and Ortega; they showed that two of their models were well-posed in Sobolev spaces and one was well-posed in analytic function spaces. For the model previously shown to have analytic solutions, we improve the theory to establish well-posedness in Sobolev spaces. This is accomplished through careful use of commutator estimates. We discuss related applications of our approach using these commutator estimates.

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Collaboration types
Domestic collaboration
International collaboration
Web of Science research areas
Mathematics
Mathematics, Applied
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