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

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2017

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https://doi.org/10.1007/s00028-016-0380-0
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Journal of Evolution Equations. 2017, 17(1), pp. 359-385. ISSN 1424-3199. eISSN 1424-3202. Available under: doi: 10.1007/s00028-016-0380-0

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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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510 Mathematik

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ISO 690KOTSCHOTE, Matthias, 2017. Spectral analysis for travelling waves in compressible two-phase fluids of Navier–Stokes–Allen–Cahn type. In: Journal of Evolution Equations. 2017, 17(1), pp. 359-385. ISSN 1424-3199. eISSN 1424-3202. Available under: doi: 10.1007/s00028-016-0380-0
BibTex
@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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