Dissipative quasi-geostrophic equations with data.
Quasi-geostrophic type equations with weak initial data.
Well-Posedness of a Semilinear Heat Equation with Weak Initial Data.
Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation
Hölder continuity of solutions of supercritical dissipative hydrodynamic transport equations
Zero-dissipation limit for nonlinear waves
Zero-Dissipation Limit for Nonlinear Waves
Evolution equations featuring nonlinearity, dispersion and dissipation are considered here. For classes of such equations that include the Korteweg-de Vries-Burgers equation and the BBM-Burgers equation, the zero dissipation limit is studied. Uniform bounds independent of the dissipation coefficient are derived and zero dissipation limit results with optimal convergence rates are established.
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