Taoufik Hmidi, Liutang Xue, Zhilong Xue
Published 2023-12-05Version 1
This paper revolves around the existence of V-states close to Rankine vortices for active scalar equations with completely monotone kernels. This allows to unify various results on this topic related to geophysical flows. A key ingredient is a new factorization formula for the spectrum using a universal function which is independent of the model. This function admits several interesting properties allowing to track the spectrum distribution.
Logarithmic spikes of gradients and uniqueness of weak solutions to a class of active scalar equations
Continuity of the solution map of some active scalar equations in Hölder and Zygmund spaces
On well-posedness of a mildly dissipative family of active scalar equations in borderline Sobolev spaces
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