Existence of multidimensional non-isothermalphase transitions in a steady van der Waals flow

Shu-Yi Zhang

doi:10.3934/dcds.2013.33.2221

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2013, Volume 33, Issue 5: 2221-2239. Doi: 10.3934/dcds.2013.33.2221

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Existence of multidimensional non-isothermal phase transitions in a steady van der Waals flow

Shu-Yi Zhang^1,

1.
Business information management school, Shanghai institute of foreign trade, 1900 Wenxiang Rd., Shanghai 201620

Received: February 28, 2011

Revised: August 31, 2012

Published: April 2013

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Abstract

This paper is concerned with the existence of multi-dimensional non-isothermal subsonic phase transitions in a steady supersonic flow with the van der Waals type state function. Due to the subsonic property, the Lax entropy inequality [15] is no longer valid for subsonic phase transitions. Hence, physical admissible planar waves are chosen by the viscosity capillarity criterion [24]. Based on the uniform stability result in [28], we perform the iteration scheme [20] and establish the existence.

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Mathematics Subject Classification: Primary: 35L45, 35L50; Secondary: 35L67.

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