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Life span of 2-D irrotational compressible fluids in the halfplane

✍ Scribed by Paolo Secchi

Publisher
John Wiley and Sons
Year
2002
Tongue
English
Weight
140 KB
Volume
25
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

We consider the Euler equations of barotropic inviscid compressible fluids in the half plane. It is well known that, as the Mach number goes to zero, the compressible flows approximate the solution of the equations of motion of inviscid, incompressible fluids. In dimension two such limit solution exists on any arbitrary time interval, with no restriction on the size of the initial velocity. It is then natural to expect the same for the compressible solution, if the Mach number is sufficiently small.

We consider smooth irrotational solutions. First, we study the life span, i.e. the largest time interval T(Ξ΅) of existence of classical solutions, when the initial data are a small perturbation of size Ξ΅from a constant state. For the proof of this result we use a combination of energy and decay estimates. Then, the estimate of the life span allows to show, by a suitable scaling of variables, the existence of irrotational solutions on any arbitrary time interval, for any small enough Mach number. Copyright Β© 2002 John Wiley & Sons, Ltd.

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