On the ill-posedness of active scalar equations with odd singular kernels

@inproceedings{Kukavica2016OnTI,
  title={On the ill-posedness of active scalar equations with odd singular kernels},
  author={Igor Kukavica and Vlad Vicol and Fei Wang},
  year={2016}
}
We consider active scalar equations with constitutive laws that are odd and very singular, in the sense that the velocity field loses more than one derivative with respect to the active scalar. We provide an example of such a constitutive law for which the equation is ill-posed: Either Sobolev solutions do not exist, from Gevrey-class datum, or the solution map fails to be Lipschitz continuous in the topology of a Sobolev space, with respect to Gevrey class perturbations in the initial datum… 
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