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• W2949253997 abstract "We consider active scalar equations $partial_t theta + nabla cdot (u , theta) = 0$, where $u = T[theta]$ is a divergence-free velocity field, and $T$ is a Fourier multiplier operator with symbol $m$. We prove that when $m$ is not an odd function of frequency, there are nontrivial, compactly supported solutions weak solutions, with Holder regularity $C^{1/9-}_{t,x}$. In fact, every integral conserving scalar field can be approximated in ${cal D}'$ by such solutions, and these weak solutions may be obtained from arbitrary initial data. We also show that when the multiplier $m$ is odd, weak limits of solutions are solutions, so that the $h$-principle for odd active scalars may not be expected." @default.
• W2949253997 created "2019-06-27" @default.
• W2949253997 creator A5076800784 @default.
• W2949253997 creator A5089255575 @default.
• W2949253997 date "2014-05-29" @default.
• W2949253997 modified "2023-09-23" @default.
• W2949253997 title "Holder Continuous Solutions of Active Scalar Equations" @default.
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• W2949253997 hasPublicationYear "2014" @default.
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