Existence and weak-strong uniqueness for the Navier-Stokes-Smoluchowski system over moving domains

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dc.contributor.advisorTrivisa, Konstantinaen_US
dc.contributor.authorDoboszczak, Stefanen_US
dc.contributor.departmentApplied Mathematics and Scientific Computationen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2016-06-22T05:59:34Z
dc.date.available2016-06-22T05:59:34Z
dc.date.issued2016en_US
dc.description.abstractThis dissertation concerns the well-posedness of the Navier-Stokes-Smoluchowski system. The system models a mixture of fluid and particles in the so-called bubbling regime. The compressible Navier-Stokes equations governing the evolution of the fluid are coupled to the Smoluchowski equation for the particle density at a continuum level. First, working on fixed domains, the existence of weak solutions is established using a three-level approximation scheme and based largely on the Lions-Feireisl theory of compressible fluids. The system is then posed over a moving domain. By utilizing a Brinkman-type penalization as well as penalization of the viscosity, the existence of weak solutions of the Navier-Stokes-Smoluchowski system is proved over moving domains. As a corollary the convergence of the Brinkman penalization is proved. Finally, a suitable relative entropy is defined. This relative entropy is used to establish a weak-strong uniqueness result for the Navier-Stokes-Smoluchowski system over moving domains, ensuring that strong solutions are unique in the class of weak solutions.en_US
dc.identifierhttps://doi.org/10.13016/M2PJ58
dc.identifier.urihttp://hdl.handle.net/1903/18294
dc.language.isoenen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pqcontrolledApplied mathematicsen_US
dc.subject.pquncontrolledcompressible fluidsen_US
dc.subject.pquncontrolledfluid-particle interactionen_US
dc.subject.pquncontrolledmoving domainsen_US
dc.subject.pquncontrolledNavier-Stokes-Smoluchowskien_US
dc.subject.pquncontrolledweak solutionsen_US
dc.subject.pquncontrolledweak-strong uniquenessen_US
dc.titleExistence and weak-strong uniqueness for the Navier-Stokes-Smoluchowski system over moving domainsen_US
dc.typeDissertationen_US

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