Abstract
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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This paper is dedicated to Jan Prüß on the occasion of his 65th birthday
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Kotschote, M. Spectral analysis for travelling waves in compressible two-phase fluids of Navier–Stokes–Allen–Cahn type. J. Evol. Equ. 17, 359–385 (2017). https://doi.org/10.1007/s00028-016-0380-0
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DOI: https://doi.org/10.1007/s00028-016-0380-0
Keywords
- Navier–Stokes–Allen–Cahn system
- Compressible fluid
- Phase field model
- Diffuse interface
- Phase transition
- Hyperbolic–parabolic system
- Travelling wave
- Spectral analysis