Propagation of regularity of level sets for a class of active transport equations. (English) Zbl 1462.35322
Summary: We prove that for any \(\alpha \in(0, 1)\), the \(C^{1 , \alpha}\) regularity of level sets for solutions to a class of active transport equations is propagated over the existence time of the solution. This extends a recent result of A. Bertozzi et al. [SIAM J. Math. Anal. 48, No. 6, 3789–3819 (2016; Zbl 1355.35110)] for patch boundary regularity for the aggregation equation.
MSC:
| 35Q49 | Transport equations |
| 35Q31 | Euler equations |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 76B47 | Vortex flows for incompressible inviscid fluids |
| 76U05 | General theory of rotating fluids |
| 35B65 | Smoothness and regularity of solutions to PDEs |
Citations:
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