✦ LIBER ✦

Global existence for one-dimensional motion of non-isentropic viscous fluids

✍ Scribed by Shigenori Yanagi

Publisher: John Wiley and Sons
Year: 1993
Tongue: English
Weight: 470 KB
Volume: 16
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.1670160902

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✦ Synopsis

Abstract

We study the p‐system with viscosity given by v~t~ − u~x~ = 0, u~t~ + p(v)~x~ = (k(v)u~x~)~x~ + f(∫ v__d__x, t), with the initial and the boundary conditions (v(x, 0), u(x,0)) = (v~0~, u~0~(x)), u(0,t) = u(X,t) = 0. To describe the motion of the fluid more realistically, many equations of state, namely the function p(v) have been proposed. In this paper, we adopt Planck's equation, which is defined only for v > b(> 0) and not a monotonic function of v, and prove the global existence of the smooth solution. The essential point of the proof is to obtain the bound of v of the form b < h(T) ⩽ v(x, t) ⩽ H(T) < ∞ for some constants h(T) and H(T).

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