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Incompressible Euler Equations and the Effect of Changes at a Distance

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Oregon State University, Corvallis, USA

    Elaine Cozzi

  2. Department of Mathematics, University of California, Riverside, USA

    James P. Kelliher

Authors
  1. Elaine Cozzi
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  2. James P. Kelliher
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Correspondence to Elaine Cozzi.

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Communicated by R. Shvydkoy

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Cozzi, E., Kelliher, J.P. Incompressible Euler Equations and the Effect of Changes at a Distance. J. Math. Fluid Mech. 18, 765–781 (2016). https://doi.org/10.1007/s00021-016-0268-3

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