| dc.contributor.author | Abbatiello, Anna | |
| dc.contributor.author | Basarić, Danica | |
| dc.contributor.author | Chaudhuri, Nilasis | |
| dc.contributor.author | Feireisl, Eduard | |
| dc.date.accessioned | 2024-09-25T12:35:53Z | |
| dc.date.available | 2024-09-25T12:35:53Z | |
| dc.date.issued | 2024-09-25 | |
| dc.identifier.uri | http://publications.mfo.de/handle/mfo/4172 | |
| dc.description.abstract | We 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.sponsorship | Acknowledgement: 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.iso | en_US | en_US |
| dc.publisher | Mathematisches Forschungsinstitut Oberwolfach | en_US |
| dc.relation.ispartofseries | Oberwolfach Preprints;2024-10 | |
| dc.subject | Navier–Stokes–Fourier System | en_US |
| dc.subject | Strong Solution | en_US |
| dc.subject | Dirichlet Problem | en_US |
| dc.subject | Local Existence | en_US |
| dc.subject | Conditional Regularity | en_US |
| dc.subject | Blow–up Criterion | en_US |
| dc.title | Local Existence and Conditional Regularity for the Navier-Stokes-Fourier System Driven by Inhomogeneous Boundary Conditions | en_US |
| dc.type | Preprint | en_US |
| dc.rights.license | Dieses 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.license | This 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.doi | 10.14760/OWP-2024-10 | |
| local.scientificprogram | OWRF 2024 | en_US |
| local.series.id | OWP-2024-10 | en_US |
| local.subject.msc | 35 | en_US |
| local.subject.msc | 76 | en_US |
| dc.identifier.ppn | 1905878362 | |
