Generalized surface quasi‐geostrophic equations with singular velocities
Generalized surface quasi‐geostrophic equations with singular velocities
Abstract This paper establishes several existence and uniqueness results for two families of active scalar equations with velocity fields determined by the scalars through very singular integrals. The first family is a generalized surface quasigeostrophic (SQG) equation with the velocity field u related to the scalar θ by $u=\nabla^\perp\Lambda^{\beta-2}\theta$ , …