Mild criticality breaking for the Navier-Stokes equations
| Autor: | Christophe Prange, Tobias Barker |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Physics
Applied Mathematics 010102 general mathematics Mathematical analysis Mathematics::Analysis of PDEs Condensed Matter Physics 01 natural sciences Supercritical fluid 010101 applied mathematics 35A99 35B44 35B65 35Q30 76D05 Computational Mathematics Arbitrarily large Nonlinear system Transfer (group theory) Mathematics - Analysis of PDEs Criticality Bounded function FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 0101 mathematics Navier–Stokes equations Nonlinear Sciences::Pattern Formation and Solitons Mathematical Physics Energy (signal processing) Analysis of PDEs (math.AP) |
| Zdroj: | Barker, T & Prange, C 2021, ' Mild criticality breaking for the Navier-Stokes equations ', Journal of Mathematical Fluid Mechanics, vol. 23, 66 . https://doi.org/10.1007/s00021-021-00591-1 Journal of Mathematical Fluid Dynamics Journal of Mathematical Fluid Dynamics, 2021, ⟨10.1007/s00021-021-00591-1⟩ |
| DOI: | 10.1007/s00021-021-00591-1 |
| Popis: | In this short paper we prove the global regularity of solutions to the Navier-Stokes equations under the assumption that slightly supercritical quantities are bounded. As a consequence, we prove that if a solution $u$ to the Navier-Stokes equations blows-up, then certain slightly supercritical Orlicz norms must become unbounded. This partially answers a conjecture recently made by Terence Tao. The proof relies on quantitative regularity estimates at the critical level and transfer of subcritical information on the initial data to arbitrarily large times. This method is inspired by a recent paper of Aynur Bulut, where similar results are proved for energy supercritical nonlinear Schr\"odinger equations. Comment: 13 pages. The current version contains an additional theorem regarding the behavior of slightly supercritical Orlicz norms near a potential blow-up time |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|