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math.AP2021
On local well-posedness of logarithmic inviscid regularizations of generalized SQG equations in borderline Sobolev spaces
Michael S. Jolly, Anuj Kumar, Vincent R. Martinez
This paper studies a family of generalized surface quasi-geostrophic (SQG) equations for an active scalar on the whole plane whose velocities have been mildly regularized, for…
math.AP2021
On the existence, uniqueness, and smoothing of solutions to the generalized SQG equations in critical Sobolev spaces
Michael S. Jolly, Anuj Kumar, Vincent R. Martinez
This paper studies the dissipative generalized surface quasi-geostrophic equations in a supercritical regime where the order of the dissipation is small relative to order of the ve…