Hyperbolic Navier-Stokes equations I : Local well-posedness

Cite This

Files in this item

Files Size Format View

There are no files associated with this item.

RACKE, Reinhard, Jürgen SAAL, 2012. Hyperbolic Navier-Stokes equations I : Local well-posedness. In: Evolution Equations & Control Theory. American Institute of Mathematical Sciences (AIMS). 1(1), pp. 195-215. eISSN 2163-2480. Available under: doi: 10.3934/eect.2012.1.195

@article{Racke2012-06Hyper-48767, title={Hyperbolic Navier-Stokes equations I : Local well-posedness}, year={2012}, doi={10.3934/eect.2012.1.195}, number={1}, volume={1}, journal={Evolution Equations & Control Theory}, pages={195--215}, author={Racke, Reinhard and Saal, Jürgen} }

<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#" xmlns:foaf="http://xmlns.com/foaf/0.1/" xmlns:void="http://rdfs.org/ns/void#" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/rdf/resource/123456789/48767"> <dc:creator>Saal, Jürgen</dc:creator> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2020-02-25T10:10:12Z</dc:date> <dcterms:issued>2012-06</dcterms:issued> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <dcterms:abstract xml:lang="eng">We replace a Fourier type law by a Cattaneo type law in the derivation of the fundamental equations of fluid mechanics. This leads to hyperbolicly perturbed quasilinear Navier-Stokes equations. For this problem the standard approach by means of quasilinear symmetric hyperbolic systems seems to fail by the fact that finite propagation speed might not be expected. Therefore a somewhat different approach via viscosity solutions is developed in order to prove higher regularity energy estimates for the linearized system. Surprisingly, this method yields stronger results than previous methods, by the fact that we can relax the regularity assumptions on the coefficients to a minimum. This leads to a short and elegant proof of a local-in-time existence result for the corresponding first order quasilinear system, hence also for the original hyperbolicly perturbed Navier-Stokes equations.</dcterms:abstract> <dc:contributor>Saal, Jürgen</dc:contributor> <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/48767"/> <dc:contributor>Racke, Reinhard</dc:contributor> <dc:creator>Racke, Reinhard</dc:creator> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2020-02-25T10:10:12Z</dcterms:available> <dc:language>eng</dc:language> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/rdf/resource/123456789/39"/> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dcterms:title>Hyperbolic Navier-Stokes equations I : Local well-posedness</dcterms:title> </rdf:Description> </rdf:RDF>

This item appears in the following Collection(s)

Search KOPS


Browse

My Account