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Existence of co-rotating and travelling vortex patches with doubly connected components for active scalar equations

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 نشر من قبل Guolin Qin
 تاريخ النشر 2021
  مجال البحث
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By applying implicit function theorem on contour dynamics, we prove the existence of co-rotating and travelling patch solutions for both Euler and the generalized surface quasi-geostrophic equation. The solutions obtained constitute a desingularization of points vortices when the size of patch support vanishes. In particular, solutions constructed in this paper consist of doubly connected components, which is essentially different from all known results.



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