The cubic Dirac equation in $H^\frac12(\R^2)$
New challenges in PDE: Deterministic dynamics and randomness in high and infinite dimensional systems October 19, 2015 - October 30, 2015
Location: SLMath: Eisenbud Auditorium
scattering results
global well-posedness
small data
massive vs massless
35J65 - Nonlinear boundary value problems for linear elliptic equations
34K30 - Functional-differential equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx]
14403
Global well-posedness and scattering for the cubic Dirac equation with small initial data in the critical space $H^{\frac12}(\R^2)$ is established. The proof is based on a sharp endpoint Strichartz estimate for the Klein-Gordon equation in dimension $n=2$, which is captured by constructing an adapted systems of coordinate frames. This is joint work with S. Herr.
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14403
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