Existence of global smooth solutions for Euler equations with symmetry (II)

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)187-203
Journal / PublicationNonlinear Analysis, Theory, Methods and Applications
Issue number1
Publication statusPublished - Jul 2000


The compressible Euler equations, which govern the gas flow surrounding a solid ball with mass M and frictional damping in n dimensions, ρt+▽·(ρu) = 0, (ρu)t+▽·ρ(u⊗u)+▽P(ρ)= -Mρx/|x|n-2αρu, where ρ, u, P and M are the density, velocity, pressure and mass of the gas, respectively, n≥3 is the dimension of x, and α>0 is the frictional constant, are examined. The pressure is assumed to satisfy the γ law and 12ργ, K is a positive constant. The existence and non-existence of global smooth solutions are studied for the initial boundary problem of the Euler equations.