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Free boundary problem for the equation of one-dimensional motion of compressible gas with density-dependent viscosity
Authors:Mari Okada  Šárka Matušů-Nečasová  Tetu Makino
Institution:(1) Present address: Department of Applied Science, Faculty of Engineering, Yamaguchi University, 755-8611 Ube, Japan;(2) Present address: Mathematical Institute, Academy of Sciences, Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic
Abstract:We consider a free boundary problem for the equation of the one-dimensional isentropic motion with density-dependent viscosity μ =b ϱ β, whereb and β are positive constants. We prove that there exists an unique weak solution globally in time, provided that β<1/3.
Sunto Si considera un problema di frontiera libera per l’equazione del moto unidimensionale isoentropico con viscosità dipendente dalla densità secondo la legge μ =b ϱ β, doveb e β sono costanti positive. Si dimostra che esiste un’unica soluzione debole globale nel tempo, purché β<1/3.
Keywords:isentropic gas  density-dependent viscosity  a free boundary problem  a global weak solution  existence  uniqueness
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