On the motion of gravity-capillary waves with odd viscosity

Abstract

We develop three asymptotic models of surface waves in a non-newtonian fluid with odd viscosity. This viscosity is also known as Hall viscosity and appears in a number of applications such as quantum Hall fluids or chiral active fluids. Besides the odd viscosity effects, these models capture both gravity and capillary forces up to quadratic interactions and take the form of nonlinear and nonlocal wave equations. Two of these models describe bidirectional waves while the third PDE studies the case of unidirectional propagation. We also prove the well-posedness of these asymptotic models in spaces of analytic functions and in Sobolev spaces. Finally, we present a number of numerical simulations for the unidirectional model.

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References in corpus (4)

• Theory of weakly damped free-surface flows: a new formulation based on potential flow solutions
• The free surface of a colloidal chiral fluid: waves and instabilities from odd stress and Hall viscosity
• An asymptotic model for internal capillary-gravity waves in deep water
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Cited by in corpus (3)

• Nonlinear shallow-water waves with vertical odd viscosity
• Well-posedness, ill-posedness, and traveling waves for models of pulsatile flow in viscoelastic vessels
• Global well-posedness and decay for viscous water wave models