Matches in SemOpenAlex for { <https://semopenalex.org/work/W2029342893> ?p ?o ?g. }
Showing items 1 to 76 of
76
with 100 items per page.
- W2029342893 endingPage "255" @default.
- W2029342893 startingPage "225" @default.
- W2029342893 abstract "The link between the Euler equations of perfect incompressible flows and the Least Action Principle has been known for a long time [1]. Solutions can be considered as geodesic curves along the manifold of volume preserving mappings. Here the “shortest path problem” is investigated. Given two different volume preserving mappings at two different times, find, for the intermediate times, an incompressible flow map that minimizes the kinetic energy (or, more generally, the Action). In its classical formulation, this problem has been solved [7] only when the two different mappings are sufficiently close in some very strong sense. In this paper, a new framework is introduced, where generalized flows are defined, in the spirit of L. C. Young, as probability measures on the set of all possible trajectories in the physical space. Then the minimization problem is generalized as the “continuous linear programming” problem that is much easier to handle. The existence problem is completely solved in the case of the <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=d> <mml:semantics> <mml:mi>d</mml:mi> <mml:annotation encoding=application/x-tex>d</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-dimensional torus. It is also shown that under natural restrictions a classical solution to the Euler equations is the unique optimal flow in the generalized framework. Finally, a link is established with the concept of measure-valued solutions to the Euler equations [6], and an example is provided where the unique generalized solution can be explicitly computed and turns out to be genuinely probabilistic." @default.
- W2029342893 created "2016-06-24" @default.
- W2029342893 creator A5001818250 @default.
- W2029342893 date "1989-01-01" @default.
- W2029342893 modified "2023-09-24" @default.
- W2029342893 title "The least action principle and the related concept of generalized flows for incompressible perfect fluids" @default.
- W2029342893 cites W1964672341 @default.
- W2029342893 cites W1984533458 @default.
- W2029342893 cites W2024268858 @default.
- W2029342893 doi "https://doi.org/10.1090/s0894-0347-1989-0969419-8" @default.
- W2029342893 hasPublicationYear "1989" @default.
- W2029342893 type Work @default.
- W2029342893 sameAs 2029342893 @default.
- W2029342893 citedByCount "132" @default.
- W2029342893 countsByYear W20293428932012 @default.
- W2029342893 countsByYear W20293428932013 @default.
- W2029342893 countsByYear W20293428932014 @default.
- W2029342893 countsByYear W20293428932015 @default.
- W2029342893 countsByYear W20293428932016 @default.
- W2029342893 countsByYear W20293428932017 @default.
- W2029342893 countsByYear W20293428932018 @default.
- W2029342893 countsByYear W20293428932019 @default.
- W2029342893 countsByYear W20293428932020 @default.
- W2029342893 countsByYear W20293428932021 @default.
- W2029342893 countsByYear W20293428932022 @default.
- W2029342893 countsByYear W20293428932023 @default.
- W2029342893 crossrefType "journal-article" @default.
- W2029342893 hasAuthorship W2029342893A5001818250 @default.
- W2029342893 hasBestOaLocation W20293428931 @default.
- W2029342893 hasConcept C121332964 @default.
- W2029342893 hasConcept C127413603 @default.
- W2029342893 hasConcept C134306372 @default.
- W2029342893 hasConcept C165818556 @default.
- W2029342893 hasConcept C2524010 @default.
- W2029342893 hasConcept C2780791683 @default.
- W2029342893 hasConcept C28826006 @default.
- W2029342893 hasConcept C33923547 @default.
- W2029342893 hasConcept C38349280 @default.
- W2029342893 hasConcept C38409319 @default.
- W2029342893 hasConcept C529865628 @default.
- W2029342893 hasConcept C62520636 @default.
- W2029342893 hasConcept C78519656 @default.
- W2029342893 hasConceptScore W2029342893C121332964 @default.
- W2029342893 hasConceptScore W2029342893C127413603 @default.
- W2029342893 hasConceptScore W2029342893C134306372 @default.
- W2029342893 hasConceptScore W2029342893C165818556 @default.
- W2029342893 hasConceptScore W2029342893C2524010 @default.
- W2029342893 hasConceptScore W2029342893C2780791683 @default.
- W2029342893 hasConceptScore W2029342893C28826006 @default.
- W2029342893 hasConceptScore W2029342893C33923547 @default.
- W2029342893 hasConceptScore W2029342893C38349280 @default.
- W2029342893 hasConceptScore W2029342893C38409319 @default.
- W2029342893 hasConceptScore W2029342893C529865628 @default.
- W2029342893 hasConceptScore W2029342893C62520636 @default.
- W2029342893 hasConceptScore W2029342893C78519656 @default.
- W2029342893 hasIssue "2" @default.
- W2029342893 hasLocation W20293428931 @default.
- W2029342893 hasOpenAccess W2029342893 @default.
- W2029342893 hasPrimaryLocation W20293428931 @default.
- W2029342893 hasRelatedWork W1555110321 @default.
- W2029342893 hasRelatedWork W2964134901 @default.
- W2029342893 hasRelatedWork W2999282378 @default.
- W2029342893 hasRelatedWork W3085801907 @default.
- W2029342893 hasRelatedWork W3106244882 @default.
- W2029342893 hasRelatedWork W3197110266 @default.
- W2029342893 hasRelatedWork W4226185989 @default.
- W2029342893 hasRelatedWork W4287668896 @default.
- W2029342893 hasRelatedWork W4293394568 @default.
- W2029342893 hasRelatedWork W4323650691 @default.
- W2029342893 hasVolume "2" @default.
- W2029342893 isParatext "false" @default.
- W2029342893 isRetracted "false" @default.
- W2029342893 magId "2029342893" @default.
- W2029342893 workType "article" @default.