Seminar Analysis: H. J. Nussenzveig Lopes (Instituto de Matematica Universidade Federal do Rio de Janeiro)

Vortex sheets for 2D incompressible ideal fluids in domains with boundary

Following the work of Krieger, Schlag, and Tataru, we construct a family of blow-up solutions with finite energy norm to the equation

∂_t²u - Δg u = |u|⁴ u.

This family has a continuous rate of blow up, but In contrast to the case where g is the Minkowski metric, the argument used to produce these solutions can only obtain blow up rates that are bounded above.

This is joint work with S. Shashahani.

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