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On bounded velocity/bounded vorticity solutions to the incompressible 2D Euler equations

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Mathematics for the Fluid Earth

In 1963 V. I. Yudovich proved the existence and uniqueness of weak solutions of the incompressible 2D Euler equations in a bounded domain assuming that the vorticity, which is the curl of velocity, is bounded. This result was later extended by A. Majda to vorticities which are bounded and integrable in the full plane. Further extensions of this result have been obtained, yet always assuming some decay of vorticity at infi nity. In a short note in 1995, Philippe Serfati gave an incomplete, yet brilliant, proof of existence and uniqueness of solutions to the 2D Euler equations in the whole plane when the initial vorticity and initial velocity are bounded, without the need for decay at in finity. In this talk I will report on work aimed at completing and extending Serfati’s result to flows in a domain exterior to an obstacle. This is joint work with David Ambrose (Drexel University), James P. Kelliher (University of California, Riverside) and Milton C. Lopes Filho (Federal University of Rio de Janeiro).

This talk is part of the Isaac Newton Institute Seminar Series series.

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