Matches in SemOpenAlex for { <https://semopenalex.org/work/W2524349054> ?p ?o ?g. }
Showing items 1 to 79 of
79
with 100 items per page.
- W2524349054 abstract "In the classic work of Beale-Kato-Majda ({[}2{]}) for the Euler equations in $mathbb{R^{mathrm{3}}}$, regularity of a solution throughout a given interval $[0,T_{*}]$ is obtained provided that the curl $omega$ satisfies $omegain L^{1}((0,T);L^{infty}(mathbb{R^{textrm{ensuremath{3}}}})$ for all $T<T_{*}$, and the arguments apply equally well to the Navier-Stokes equations (NSE) in $mathbb{R^{mathrm{3}}}$. The spatial $L^{infty}$-criterion imposed on the curl was generalized to other function spaces by various authors ({[}9{]}, {[}10{]}, {[}11{]}). In {[}8{]} regularity results of this type are obtained on localized balls. In this paper for the NSE case and on general bounded domains $Omega$ in $mathbb{R^{mathrm{3}}}$, we obtain a regularity result of BKM type that allows $omega$ to be a distribution. Specifically, we show that if $u$ is a Leray solution of the 3-D NSE on the interval $(0,T)$ and if $omegain L^{s}((0,T);H^{-1,p}(Omega))$ where $frac{2}{s}+frac{3}{p}=1$ for some $pin(3,infty]$, then $u$ is a regular solution on $left(0,T]right)$; in particular for $p=infty$ we have a regular solution when $omegain L^{2}((0,T);H^{-1,infty}(Omega))$, which directly strengthens the results in {[}2{]} by one order of (negative) derivative in terms of the spatial criteria for regularity. Our results thus impose more stringent conditions on time than the BKM results and their generalizations described above, but as far as we are aware the results here represent the first of BKM type for the NSE that allow $omega$ to spatially be a distribution." @default.
- W2524349054 created "2016-10-07" @default.
- W2524349054 creator A5050079930 @default.
- W2524349054 date "2014-05-14" @default.
- W2524349054 modified "2023-09-27" @default.
- W2524349054 title "Regularity Criteria of BKM type in Distributional Spaces for the 3-D Navier-Stokes Equations on Bounded Domains" @default.
- W2524349054 cites W1985817879 @default.
- W2524349054 cites W1988761547 @default.
- W2524349054 cites W1996952201 @default.
- W2524349054 cites W2017780476 @default.
- W2524349054 cites W2025578652 @default.
- W2524349054 cites W2035682062 @default.
- W2524349054 cites W2045928936 @default.
- W2524349054 cites W2051926666 @default.
- W2524349054 cites W2063364248 @default.
- W2524349054 cites W2073676149 @default.
- W2524349054 cites W2151847866 @default.
- W2524349054 cites W3038830718 @default.
- W2524349054 hasPublicationYear "2014" @default.
- W2524349054 type Work @default.
- W2524349054 sameAs 2524349054 @default.
- W2524349054 citedByCount "0" @default.
- W2524349054 crossrefType "posted-content" @default.
- W2524349054 hasAuthorship W2524349054A5050079930 @default.
- W2524349054 hasConcept C114614502 @default.
- W2524349054 hasConcept C121332964 @default.
- W2524349054 hasConcept C134306372 @default.
- W2524349054 hasConcept C147663694 @default.
- W2524349054 hasConcept C18903297 @default.
- W2524349054 hasConcept C199360897 @default.
- W2524349054 hasConcept C2777299769 @default.
- W2524349054 hasConcept C2779557605 @default.
- W2524349054 hasConcept C33923547 @default.
- W2524349054 hasConcept C34388435 @default.
- W2524349054 hasConcept C37914503 @default.
- W2524349054 hasConcept C41008148 @default.
- W2524349054 hasConcept C62520636 @default.
- W2524349054 hasConcept C86803240 @default.
- W2524349054 hasConceptScore W2524349054C114614502 @default.
- W2524349054 hasConceptScore W2524349054C121332964 @default.
- W2524349054 hasConceptScore W2524349054C134306372 @default.
- W2524349054 hasConceptScore W2524349054C147663694 @default.
- W2524349054 hasConceptScore W2524349054C18903297 @default.
- W2524349054 hasConceptScore W2524349054C199360897 @default.
- W2524349054 hasConceptScore W2524349054C2777299769 @default.
- W2524349054 hasConceptScore W2524349054C2779557605 @default.
- W2524349054 hasConceptScore W2524349054C33923547 @default.
- W2524349054 hasConceptScore W2524349054C34388435 @default.
- W2524349054 hasConceptScore W2524349054C37914503 @default.
- W2524349054 hasConceptScore W2524349054C41008148 @default.
- W2524349054 hasConceptScore W2524349054C62520636 @default.
- W2524349054 hasConceptScore W2524349054C86803240 @default.
- W2524349054 hasLocation W25243490541 @default.
- W2524349054 hasOpenAccess W2524349054 @default.
- W2524349054 hasPrimaryLocation W25243490541 @default.
- W2524349054 hasRelatedWork W1482266505 @default.
- W2524349054 hasRelatedWork W1552072083 @default.
- W2524349054 hasRelatedWork W1552560119 @default.
- W2524349054 hasRelatedWork W2540837837 @default.
- W2524349054 hasRelatedWork W2736399449 @default.
- W2524349054 hasRelatedWork W2747348004 @default.
- W2524349054 hasRelatedWork W2790778170 @default.
- W2524349054 hasRelatedWork W2802673282 @default.
- W2524349054 hasRelatedWork W2803585723 @default.
- W2524349054 hasRelatedWork W2899914918 @default.
- W2524349054 hasRelatedWork W2948482226 @default.
- W2524349054 hasRelatedWork W2949910056 @default.
- W2524349054 hasRelatedWork W2951001422 @default.
- W2524349054 hasRelatedWork W2953154351 @default.
- W2524349054 hasRelatedWork W2963578422 @default.
- W2524349054 hasRelatedWork W3098512942 @default.
- W2524349054 hasRelatedWork W3099946881 @default.
- W2524349054 hasRelatedWork W3105117118 @default.
- W2524349054 hasRelatedWork W3194235509 @default.
- W2524349054 hasRelatedWork W2791352819 @default.
- W2524349054 isParatext "false" @default.
- W2524349054 isRetracted "false" @default.
- W2524349054 magId "2524349054" @default.
- W2524349054 workType "article" @default.