Application of harmonic analysis techniques to regularity problems of dissipative equations

2018/09/17 by Mimi Dai, Han Liu, Dai, Mimi +1
Engineering · Mathematics · #35Q35 #76D03 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions #math.AP #msc:35Q35 #msc:76D03

paper · pdf · doi:10.48550/arxiv.1809.06454

arxiv created 2018/09/17 · openalex publication_date 2018/09/17 · arxiv updated 2018/09/19 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28

Abstract

We discuss recent advances in the regularity problem of a variety of fluid equations and systems. The purpose is to illustrate the advantage of harmonic analysis techniques in obtaining sharper conditional regularity results when compared to classical energy methods.

Citations

• Inéquations en thermoélasticité et magnétohydrodynamique
• Sur le mouvement d'un liquide visqueux emplissant l'espace
• Some mathematical questions related to the mhd equations

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• Regularity theory for the dissipative solutions of the MHD equations
• Quantitative partial regularity of the Navier-Stokes equations and applications
• Conserved quantities and regularity in fluid dynamics
• A unified approach to regularity problems for the 3D Navier-Stokes and Euler equations: the use of Kolmogorov's dissipation range
• Intermittency and Dissipation Regularity in Turbulence