Spectral analysis for travelling waves in compressible two-phase fluids of Navier–Stokes–Allen–Cahn type

Spectral analysis for travelling waves in compressible two-phase fluids of Navier–Stokes–Allen–Cahn type

This is the first part of two papers whose purpose is to investigate stability of travelling wave solutions to the so-called Navier–Stokes–Allen–Cahn system. This set of equations is a combination of the Navier–Stokes equations for compressible fluids supplemented with a phase field description of A...

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Veröffentlicht in:Journal of evolution equations 2017-03, Vol.17 (1), p.359-385
1. Verfasser: Kotschote, Matthias
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Navier-Stokes equations
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description This is the first part of two papers whose purpose is to investigate stability of travelling wave solutions to the so-called Navier–Stokes–Allen–Cahn system. This set of equations is a combination of the Navier–Stokes equations for compressible fluids supplemented with a phase field description of Allen–Cahn type. The main part of this work deals with studying the problem obtained by linearizing the NSAC system around so-called standing waves. The main results are (1) local well-posedness of the linearized equations and (2) a detailed description of the point and essential spectrum. As a by-product, we obtain analyticity of the associated semigroup.
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Mathematics
Mathematics and Statistics
Navier-Stokes equations
title Spectral analysis for travelling waves in compressible two-phase fluids of Navier–Stokes–Allen–Cahn type
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