Incompressible Euler Equations and the Effect of Changes at a Distance

Because pressure is determined globally for the incompressible Euler equations, a localized change to the initial velocity will have an immediate effect throughout space. For solutions to be physically meaningful, one would expect such effects to decrease with distance from the localized change, giv...

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Bibliographic Details
Published in:Journal of mathematical fluid mechanics 2016-12, Vol.18 (4), p.765-781
Main Authors: Cozzi, Elaine, Kelliher, James P.
Format: Article
Language:English
Subjects:
Classical and Continuum Physics
Decay
Euler-Lagrange equation
Eulers equations
Fluid mechanics
Fluid- and Aerodynamics
Mathematical analysis
Mathematical Methods in Physics
Physics
Physics and Astronomy
Stability
Theoretical mathematics
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Summary:Because pressure is determined globally for the incompressible Euler equations, a localized change to the initial velocity will have an immediate effect throughout space. For solutions to be physically meaningful, one would expect such effects to decrease with distance from the localized change, giving the solutions a type of stability. Indeed, this is the case for solutions having spatial decay, as can be easily shown. We consider the more difficult case of solutions lacking spatial decay, and show that such stability still holds, albeit in a somewhat weaker form.
ISSN:1422-6928
1422-6952
DOI:10.1007/s00021-016-0268-3