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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References

SHOWING 1-7 OF 7 REFERENCES
Euler evolution for singular initial data and vortex theory
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,
Evolution of two concentrated vortices in a two-dimensional bounded domain
We prove that two initially concentrated vortices with opposite vorticity of an incompressible ideal fluid moving in a two-dimensional bounded domain, remain concentrated during the time. The motion
Vortex Methods in Two-Dimensional Fluid Dynamics
Euler equations.- Vortex model.- An existence theorem for Euler equations.- Further considerations on vortex model.- A mean field limit.- Navier-Stokes equations.- Diffusion process and Navier-Stokes
Mathematical and Physical Papers
Sir George Stokes (1819–1903) established the science of hydrodynamics with his law of viscosity describing the velocity of a small sphere through a viscous fluid. He published no books, but was a
On the evolution of a concentrated vortex in an ideal fluid
Planar Navier-Stokes flow for singular initial data