Blowup for the 3D compressible Euler equations. (March 2016)

• Record Type: Journal Article
• Authors: Zhu, Xusheng; Tu, Aihua; Fu, Chunyan
• Is Part Of: Nonlinear analysis. Volume 133(2016)
• Page Start: 51
• Page End: 60
• Publication Date: 2016-03
• Subjects: 35L50 -- 35L65 -- 35L67; Compressible 3D Euler equations -- Cauchy problem -- C1 solution -- Blowup -- Functional methods; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.11.021
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We establish several results about the blowup of the solutions for the Cauchy problem of the 3D compressible Euler equations, under some assumptions on weighed functionals associated with the initial momentum that they are large enough to develop singularities. Especially we prove the blowup results without the condition η ( 0 ) = ∫ [ ρ ( x, 0 ) e S ( x, 0 ) γ − ρ ̄ e S ̄ γ ] d x ≥ 0, while it is an essential condition in the well-known result obtained by Thomas C. Sideris. Highlights: Comparing to Sideris' result in 1985, a blowup result is obtained without m ( 0 ) ≥ 0 . A blowup result is obtained without the condition η ( 0 ) ≥ 0, which is essential before. Several blowup results are obtained by calculating some modified functionals.