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dc.contributor.authorAbbatiello, Anna
dc.contributor.authorBasarić, Danica
dc.contributor.authorChaudhuri, Nilasis
dc.contributor.authorFeireisl, Eduard
dc.date.accessioned2024-09-25T12:35:53Z
dc.date.available2024-09-25T12:35:53Z
dc.date.issued2024-09-25
dc.identifier.urihttp://publications.mfo.de/handle/mfo/4172
dc.description.abstractWe consider the Navier–Stokes–Fourier system with general inhomogeneous Dirichlet–Neumann boundary conditions. We propose a new approach to the local well-posedness problem based on conditional regularity estimates. By conditional regularity we mean that any strong solution belonging to a suitable class remains regular as long as its amplitude remains bounded. The result holds for general Dirichlet-Neumann boundary conditions provided the material derivative of the velocity field vanishes on the boundary of the physical domain. As a corollary of this result we obtain: Blow up criteria for strong solutions; Local existence of strong solutions in the optimal Lp - Lq framework; Alternative proof of the existing results on local well posedness.en_US
dc.description.sponsorship∗The work of A.A. is performed under the auspices of the Italian National Group of the Mathematical Physics (GNFM) of INdAM. †The work of D.B. was supported by the PRIN project 2022 “Partial differential equations and related geometric-functional inequalities”, financially supported by the EU, in the framework of the “Next Generation EU initiative”. The Department of Mathematics of Politecnico di Milano is supported by MUR “Excellence Department 2023-2027”. ‡The work of N.C. was supported by the “Excellence Initiative Research University (IDUB)” program at the University of Warsaw. §The work of E.F. was partially supported by the Czech Sciences Foundation (GAˇCR), Grant Agreement 24–11034S. The Institute of Mathematics of the Academy of Sciences of the Czech Republic is supported by RVO:67985840. E.F. is member of the Neˇcas Center for Mathematical Modelling.en_US
dc.description.sponsorshipAcknowledgement: This work was done while the authors were participating in the Oberwolfach Research Fellows Program at Mathematisches Forschungsinstitut Oberwolfach. They warmly thank the Institute for its kind hospitality and the excellent research environment it provided.
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2024-10
dc.subjectNavier–Stokes–Fourier Systemen_US
dc.subjectStrong Solutionen_US
dc.subjectDirichlet Problemen_US
dc.subjectLocal Existenceen_US
dc.subjectConditional Regularityen_US
dc.subjectBlow–up Criterionen_US
dc.titleLocal Existence and Conditional Regularity for the Navier-Stokes-Fourier System Driven by Inhomogeneous Boundary Conditionsen_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2024-10
local.scientificprogramOWRF 2024en_US
local.series.idOWP-2024-10en_US
local.subject.msc35en_US
local.subject.msc76en_US
dc.identifier.ppn1905878362


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