Matches in SemOpenAlex for { <https://semopenalex.org/work/W2027500786> ?p ?o ?g. }
Showing items 1 to 86 of
86
with 100 items per page.
- W2027500786 endingPage "638" @default.
- W2027500786 startingPage "607" @default.
- W2027500786 abstract "Forn×n systems of conservation laws in one dimension without source terms, the existence of global weak solutions was proved by Glimm [1]. Glimm constructed approximate solutions using a difference scheme by solving a class of Riemann problems. In this paper, we consider the Cauchy problem for the Euler equations in the spherically symmetric case when the initial data are small perturbations of the trivial solution, i.e.,u≡0 and ρ≡constant, whereu is velocity and ρ is density. We show that this Cauchy problem can be reduced to an ideal nonlinear problem approximately. If we assume all the waves move at constant speeds in the ideal problem, by using Glimm's scheme and an integral approach to sum the contributions of the reflected waves that correspond to each path through the solution, we get uniform bounds on theL ∞ norm and total variational norm of the solutions for all time. The geometric effects of spherical symmetry leads to a non-integrable source term in the Euler equations. Correspondingly, we consider an infinite reflection problem and solve it by considering the cancellations between reflections of different orders in our ideal problem. Thus we view this as an analysis of the interaction effects at the quadratic level in a nonlinear model problem for the Euler equations. Although it is far more difficult to obtain estimates in the exact solutions of the Euler equations due to the problem of controlling the time at which the cancellations occur, we believe that this analysis of the wave behaviour will be the first step in solving the problem of existence of global weak solutions for the spherically symmetric Euler equations outside of fixed ball." @default.
- W2027500786 created "2016-06-24" @default.
- W2027500786 creator A5088254209 @default.
- W2027500786 date "1995-08-01" @default.
- W2027500786 modified "2023-09-23" @default.
- W2027500786 title "A functional integral approach to shock wave solutions of Euler equations with spherical symmetry" @default.
- W2027500786 cites W1601100443 @default.
- W2027500786 cites W1966318025 @default.
- W2027500786 cites W1982305009 @default.
- W2027500786 cites W1984735519 @default.
- W2027500786 cites W1995156763 @default.
- W2027500786 cites W1996669375 @default.
- W2027500786 cites W2006424975 @default.
- W2027500786 cites W2006608560 @default.
- W2027500786 cites W2026388260 @default.
- W2027500786 doi "https://doi.org/10.1007/bf02104680" @default.
- W2027500786 hasPublicationYear "1995" @default.
- W2027500786 type Work @default.
- W2027500786 sameAs 2027500786 @default.
- W2027500786 citedByCount "16" @default.
- W2027500786 countsByYear W20275007862012 @default.
- W2027500786 countsByYear W20275007862013 @default.
- W2027500786 countsByYear W20275007862015 @default.
- W2027500786 countsByYear W20275007862017 @default.
- W2027500786 countsByYear W20275007862019 @default.
- W2027500786 countsByYear W20275007862020 @default.
- W2027500786 countsByYear W20275007862022 @default.
- W2027500786 crossrefType "journal-article" @default.
- W2027500786 hasAuthorship W2027500786A5088254209 @default.
- W2027500786 hasBestOaLocation W20275007862 @default.
- W2027500786 hasConcept C121332964 @default.
- W2027500786 hasConcept C134306372 @default.
- W2027500786 hasConcept C153635880 @default.
- W2027500786 hasConcept C158622935 @default.
- W2027500786 hasConcept C17744445 @default.
- W2027500786 hasConcept C191795146 @default.
- W2027500786 hasConcept C199479865 @default.
- W2027500786 hasConcept C199539241 @default.
- W2027500786 hasConcept C200741047 @default.
- W2027500786 hasConcept C26955809 @default.
- W2027500786 hasConcept C2781217745 @default.
- W2027500786 hasConcept C33923547 @default.
- W2027500786 hasConcept C3445786 @default.
- W2027500786 hasConcept C38409319 @default.
- W2027500786 hasConcept C40709475 @default.
- W2027500786 hasConcept C62520636 @default.
- W2027500786 hasConcept C62884695 @default.
- W2027500786 hasConceptScore W2027500786C121332964 @default.
- W2027500786 hasConceptScore W2027500786C134306372 @default.
- W2027500786 hasConceptScore W2027500786C153635880 @default.
- W2027500786 hasConceptScore W2027500786C158622935 @default.
- W2027500786 hasConceptScore W2027500786C17744445 @default.
- W2027500786 hasConceptScore W2027500786C191795146 @default.
- W2027500786 hasConceptScore W2027500786C199479865 @default.
- W2027500786 hasConceptScore W2027500786C199539241 @default.
- W2027500786 hasConceptScore W2027500786C200741047 @default.
- W2027500786 hasConceptScore W2027500786C26955809 @default.
- W2027500786 hasConceptScore W2027500786C2781217745 @default.
- W2027500786 hasConceptScore W2027500786C33923547 @default.
- W2027500786 hasConceptScore W2027500786C3445786 @default.
- W2027500786 hasConceptScore W2027500786C38409319 @default.
- W2027500786 hasConceptScore W2027500786C40709475 @default.
- W2027500786 hasConceptScore W2027500786C62520636 @default.
- W2027500786 hasConceptScore W2027500786C62884695 @default.
- W2027500786 hasIssue "3" @default.
- W2027500786 hasLocation W20275007861 @default.
- W2027500786 hasLocation W20275007862 @default.
- W2027500786 hasOpenAccess W2027500786 @default.
- W2027500786 hasPrimaryLocation W20275007861 @default.
- W2027500786 hasRelatedWork W1958605926 @default.
- W2027500786 hasRelatedWork W2027500786 @default.
- W2027500786 hasRelatedWork W2029811565 @default.
- W2027500786 hasRelatedWork W2037486993 @default.
- W2027500786 hasRelatedWork W2113744788 @default.
- W2027500786 hasRelatedWork W2809355469 @default.
- W2027500786 hasRelatedWork W3005306692 @default.
- W2027500786 hasRelatedWork W4229727126 @default.
- W2027500786 hasRelatedWork W4240076417 @default.
- W2027500786 hasRelatedWork W4251559080 @default.
- W2027500786 hasVolume "171" @default.
- W2027500786 isParatext "false" @default.
- W2027500786 isRetracted "false" @default.
- W2027500786 magId "2027500786" @default.
- W2027500786 workType "article" @default.