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arXiv · 2404.18455

Oscillations in Compressible Navier-Stokes and Homogenization in Phase Transition problems

Athanasios E. Tzavaras
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Abstract

In the first part of this article we present some exact solutions for special hyperbolic-parabolic systems with sustained oscillations induced by the initial data, most notably the compressible Navier-Stokes system with non-monotone pressure. This part complements \cite{Tzavaras23} where such examples are extensively studied. The second part deals with the problem of homogenization for one-dimensional models describing phase transitions for viscoelastic materials . Ideas from the kinetic formulation of conservation laws are employed to derive effective equations that describe the propagation of oscillations.

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Athanasios E. Tzavaras. 2024-04-29. Oscillations in Compressible Navier-Stokes and Homogenization in Phase Transition problems. https://arxiv.org/abs/2404.18455

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