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

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-Belinchón 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.