Weakly Nonlinear-Dissipative Approximations of Hyperbolic-Parabolic Systems with Entropy

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dc.creatorJiang, Ning
dc.creatorLevermore, C. David
dc.date2009-04-22
dc.date.accessioned2026-07-07T13:07:49Z
dc.date.available2026-07-07T13:07:49Z
dc.descriptionHyperbolic-parabolic systems have spatially homogenous stationary states. When the dissipation is weak, one can derive weakly nonlinear-dissipative approximations that govern perturbations of these constant states. These approximations are quadratically nonlinear. When the original system has an entropy, the approximation is formally dissipative in a natural Hilbert space. We show that when the approximation is strictly dissipative it has global weak solutions for all initial data in that Hilbert space. We also prove a weak-strong uniqueness theorem for it. In addition, we give a Kawashima type criterion for this approximation to be strictly dissipative. We apply the theory to the compressible Navier-Stokes system.
dc.description29 pages, submitted
dc.identifierhttps://arxiv.org/abs/0904.3572
dc.identifierhttp://arxiv.org/abs/0904.3572
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/228219
dc.subjectAnalysis of PDEs
dc.titleWeakly Nonlinear-Dissipative Approximations of Hyperbolic-Parabolic Systems with Entropy
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