LOGARITHMICALLY REGULARIZED INVISCID MODELS IN BORDERLINE SOBOLEV SPACES DONGHO CHAE AND JIAHONG WU Dedicated to Professor Peter Constantin on the occasion of his sixtieth birthday

Several inviscid models in hydrodynamics and geophysics such as the incompressible Euler vorticity equations, the surface quasi-geostrophic equation and the Boussinesq equations are not known to have even local well-posedness in the corresponding borderline Sobolev spaces. Here H is referred to as a borderline Sobolev space if the L∞-norm of the gradient of the velocity is not bounded by the H-norm of the solution but by the H -norm for any s̃ > s. This paper establishes the local well-posedness of the logarithmically regularized counterparts of these inviscid models in the borderline Sobolev spaces.