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On the Existence of Two-Dimensional, Localized, Rotating, Self-Similar Vortical Structures
SIAM Journal on Applied Mathematics
We prove that a Gaussian monopole, also known as the Lamb-Oseen vortex, is the only localized, rotating, self-similar solution to the two-dimensional, incompressible Navier-Stokes equations where level sets of vorticity and corotating streamfunction coincide. Our definition of self-similarity is restricted to the natural linear combination of space, time and viscous diffusion. We arrive at this conclusion by analytically determining the azimuthal Fourier modes for all possible solutions to thisdoi:10.1137/s0036139901386570 fatcat:t6s4cjlawbc2vpl7olbwlyassa