Regular solutions to the fractional Euler alignment system in the Besov\n spaces framework

2018/04/20 by Raphaël Danchin, Piotr B. Mucha, Danchin, Raphaël +5 · 3 citations
Engineering · Mathematics · #35B65 #35Q31 #35R11 #76N10 #82C22 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1804.07611

openalex publication_date 2018/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We here construct (large) local and small global-in-time regular unique\nsolutions to the fractional Euler alignment system in the whole space mathbb\nR^d, in the case where the deviation of the initial density from a constant\nis sufficiently small. Our analysis strongly relies on the use of Besov spaces\nof the type L¹(0,T; B^s_p,1), which allow to get time independent\nestimates for the density even though it satisfies a transport equation with no\ndamping. Our choice of a functional setting is not optimal but aims at\nproviding a transparent and accessible argumentation.\n

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