# American Institute of Mathematical Sciences

May  2013, 33(5): 2221-2239. doi: 10.3934/dcds.2013.33.2221

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

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

Received  March 2011 Revised  September 2012 Published  December 2012

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 Due to the subsonic property, the Lax entropy inequality [15] is no longer valid for subsonic phase transitions.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.
Citation: Shu-Yi Zhang. Existence of multidimensional non-isothermal phase transitions in a steady van der Waals flow. Discrete & Continuous Dynamical Systems - A, 2013, 33 (5) : 2221-2239. doi: 10.3934/dcds.2013.33.2221
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