Phase Space Analysis of Partial Differential Equations

Wave Maps, global regularity for smooth initial data small in the critical Sobolev space

speaker: Joachim Krieger (Harward University)

abstract: I outlined the techniques that led to the recent result of myself and D. Tataru on global regularity of Wave Maps originating on R^{n+1}, n\geq 2, to a broad class of targets encompassing all compact ones as well as hyperbolic spaces, provided the initial data are smooth and small in the critical Sobolev space \dot{H}^{n2}. The techniques are both analytic (X^{s,\theta}-type spaces, null-frame spaces, extensive use of microlocalization, multilinear null-form estimates) as well as geometric (technique of moving frames, use of the Coulomb Gauge, Hodge type decompositions, vector fields method). I also related this problem to other semilinear equations, such as Yang-Mills or MKG.

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