A coupling between a non--linear 1D compressible--incompressible        limit and the 1D $p$--system in the non smooth case

Rinaldo M.  Colombo; Graziano  Guerra

doi:10.3934/nhm.2016.11.313

Article Contents

2016, Volume 11, Issue 2: 313-330. Doi: 10.3934/nhm.2016.11.313

This issue Previous Article Logarithmic estimates for continuity equations Next Article BV regularity near the interface for nonuniform convex discontinuous flux

A coupling between a non--linear 1D compressible--incompressible limit and the 1D $p$--system in the non smooth case

Rinaldo M. Colombo^1, and
Graziano Guerra^2,

1.
INdAM Unit c/o DII, Università degli Studi di Brescia, Via Branze 38, 25123 Brescia
2.
Dipartimento di Matematica e Applicazioni Via Roberto Cozzi, 55 - 20125 Milano

Received: April 2015

Published online: March 2016

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Abstract

We consider two compressible immiscible fluids in one space dimension and in the isentropic approximation. The first fluid is surrounded and in contact with the second one. As the sound speed of the first fluid diverges to infinity, we present the proof of rigorous convergence for the fully non--linear compressible to incompressible limit of the coupled dynamics of the two fluids. A linear example is considered in detail, where fully explicit computations are possible.

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Mathematics Subject Classification: Primary: 35L65, 35Q35; Secondary: 35Q31.

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References

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