References & Citations
Mathematics > Analysis of PDEs
Title: Propagation of regularity for transport equations. A Littlewood-Paley approach
(Submitted on 21 Mar 2022 (v1), last revised 26 Apr 2024 (this version, v3))
Abstract: It is known that linear advection equations with Sobolev velocity fields have very poor regularity properties: Solutions propagate only derivatives of logarithmic order, which can be measured in terms of suitable Gagliardo seminorms. We propose a new approach to the study of regularity that is based on Littlewood-Paley theory, thus measuring regularity in terms of Besov norms. We recover the results that are available in the literature and extend these optimally to the diffusive setting. As a consequence, we derive sharp bounds on rates of convergence in the zero-diffusivity limit.
Submission history
From: Christian Seis [view email][v1] Mon, 21 Mar 2022 10:32:52 GMT (22kb)
[v2] Fri, 9 Jun 2023 08:12:33 GMT (22kb)
[v3] Fri, 26 Apr 2024 07:08:11 GMT (22kb)
Link back to: arXiv, form interface, contact.