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
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Journal of Evolution Equations ; 17 (2017), 1. - S. 359-385. - ISSN 1424-3199. - eISSN 1424-3202
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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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KOTSCHOTE, Matthias, 2017. Spectral analysis for travelling waves in compressible two-phase fluids of Navier–Stokes–Allen–Cahn type. In: Journal of Evolution Equations. 17(1), pp. 359-385. ISSN 1424-3199. eISSN 1424-3202. Available under: doi: 10.1007/s00028-016-0380-0BibTex
@article{Kotschote2017-03Spect-38903, year={2017}, doi={10.1007/s00028-016-0380-0}, title={Spectral analysis for travelling waves in compressible two-phase fluids of Navier–Stokes–Allen–Cahn type}, number={1}, volume={17}, issn={1424-3199}, journal={Journal of Evolution Equations}, pages={359--385}, author={Kotschote, Matthias} }
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