Euler evolution for singular initial data and vortex theory: A global solution

@article{Marchioro1988EulerEF,
  title={Euler evolution for singular initial data and vortex theory: A global solution},
  author={Carlo Marchioro},
  journal={Communications in Mathematical Physics},
  year={1988},
  volume={116},
  pages={45-55}
}
  • C. Marchioro
  • Published 1 March 1988
  • Mathematics, Physics
  • Communications in Mathematical Physics
We study the evolution of a two-dimensional, incompressible, ideal fluid in a case in which the vorticity is concentrated in small disjoint regions and we prove, globally in time, its connection with the vortex model. 
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30 Citations
Background Citations
12
Methods Citations
1
Results Citations
2

30 Citations

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We study the time evolution of the support of a vortex patch evolving in ℝ2 according to the Euler Equation for an incompressible fluid and we bound its growth. Furthermore we discuss the same…
Long Time Evolution of Concentrated Euler Flows with Planar Symmetry
TLDR
A toy model is analyzed that shows a similar behavior to an incompressible Euler fluid with planar symmetry when the vorticity is initially concentrated in small disks, showing that in some cases this happens for quite long times.
On the vanishing viscosity limit for two-dimensional Navier–Stokes equations with singlular initial data
We study the solutions of the Navier–Stokes equations when the initial vorticity is concentrated in small disjoint regions of diameter ϵ. We prove that they converge, uniformily in ϵ. for vanishing…
On the motion of a vortex ring with a sharply concentrated vorticity
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On the Inviscid Limit for a Viscous Active Scalar Flow with Concentrated Fields
Euler evolution of a concentrated vortex in planar bounded domains
In this paper, we consider the time evolution of an ideal fluid in a planar bounded domain. We prove that if the initial vorticity is supported in a sufficiently small region with diameter…
Concentrated Euler flows and point vortex model
This paper is an improvement of previous results on concentrated Euler flows and their connection with the point vortex model. Precisely, we study the time evolution of an incompressible two…
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References

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We study the evolution of a two dimensional, incompressible, ideal fluid in a case in which the vorticity is concentrated in small, disjoint regions of the physical space. We prove, for short times,…
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