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Joint Princeton-Rutgers Seminar on Analysis of Fluids

Viscous perturbations to discontinuous solutions of the compressible Euler equation

Alexis Vasseur, University of Texas at Austin

Location:  Hill 705, Rutgers University
Date & time: Tuesday, 02 April 2024 at 1:40PM - 2:40PM

The compressible Euler equation can lead to the emergence of shocks-discontinuities in finite time, notably observed behind supersonic planes.  A very natural way to justify these singularities involves studying solutions as inviscid limits of Navier-Stokes solutions with evanescent viscosities.The mathematical study of this problem is however very difficult because of the destabilization effect of the viscosities.

 

Bianchini and Bressan proved the inviscid limit to small BV solutions using the so-called artificial viscosities in 2004. However, until very recently, achieving this limit with physical viscosities remained an open question.

 

 In this presentation, we will  present the basic ideas of  classical mathematical theories to compressible fluid mechanics and introduce the recent a-contraction with shifts method. This method is employed to describe the physical inviscid limit in the context of the barotropic Euler equation.

 

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