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2014•Journal of Xiamen UniversityRequires access

Blowup of the Axis-symmetric Solutions for the IBVP of the Compressible Isentropic Euler Equations with Damping

Zhu Xu-shen

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Abstract

In this paper we study the blowup of axis-symmetric solutions for the initial-boundary value problem of the compressible isentropic Euler equation in R3.We show by functional methods that classical solutions will blow up before a certain time under the assumption that the functional associated with the initial velocity is sufficiently large.Compared to the non-damping case,the damping increased the difficulty of the blowup of the classical solution.

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What this paper is about

In this paper we study the blowup of axis-symmetric solutions for the initial-boundary value problem of the compressible isentropic Euler equation in R3.We show by functional methods that classical solutions will blow up before a certain time under the assumption that the functional associated with the initial velocity is sufficiently large.Compared to the non-damping case,the damping increased the difficulty of the blowup of the classical solution.

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Available abstract

In this paper we study the blowup of axis-symmetric solutions for the initial-boundary value problem of the compressible isentropic Euler equation in R3.We show by functional methods that classical solutions will blow up before a certain time under the assumption that the functional associated with the initial velocity is sufficiently large.Compared to the non-damping case,the damping increased the difficulty of the blowup of the classical solution.

Key concepts: Isentropic process, Compressibility, Euler equations, Euler's formula, Mathematical analysis, Mathematics, Boundary value problem, Compressible flow

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