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# Singular limits of the compressible fluid models

Nilasis Chaudhuri, Technische Universitat, Berlin
 Speaker Nilasis Chaudhuri, Technische Universitat, Berlin Dec 31, 2019 from 04:00 PM to 05:00 PM LH 006 vCal iCal

Abstract: In this talk I explain the study of singular limits for a scaled barotropic Euler system modelling a rotating, compressible and inviscid fluid, where Mach number $$=\epsilon^m$$, Rossby number $$=\epsilon$$ and Froude number $$=\epsilon^n$$ are proportional to a small parameter $$\epsilon\rightarrow 0$$ and $$m,n\in \mathbb{N}$$. I consider the fluid is confined to an infinite slab, the limit behaviour is identified as the incompressible Euler system. For well--prepared initial data, the convergence is shown on the life span time interval of the strong solutions of the target system, whereas a class of generalized dissipative solutions is considered for the primitive system. The technique can be adapted to the compressible Navier--Stokes system in the subcritical range of the adiabatic exponent $$\gamma$$ with $$1<\gamma\leq\frac{3}{2}$$, where the weak solutions are not known to exist.

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