Sharper Total Variation Bounds for the P-System of Fluid Dynamics

Tsikkou, Charis

doi:10.1142/s0219891611002391

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2014

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“…The polygonal scheme was first established by Dafermos in [11] in the study of scalar conservation law then was modified by Diperna for system of conservation laws. The scheme has been widely used for the well-posedness and behaviors of hyperbolic conservation laws [1,10,20].…”

Section: For Analysis and Examplesmentioning

confidence: 99%

Lower bound of density for Lipschitz continuous solutions in the isentropic gas dynamics

Chen,

Pan,

Zhu

2014

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For the Euler equations of isentropic gas dynamics in one space dimension, also knowns as p-system in Lagrangian coordinate, it is known that the density can be arbitrarily close to zero as time goes to infinity, even when initial density is uniformly away from zero. In this paper, for uniform positive initial density, we prove the density in any Lipschitz continuous solutions for Cauchy problem has a sharp positive lower bound in the order of O( 11+t ), which is identified by explicit examples in [9].

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Section: For Analysis and Examplesmentioning

confidence: 99%