Analysis seminar: Timothy Candy
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Speaker: Timothy Candy, Chapman Fellow, Imperial College London, UK
Title: Critical well-posedness for the Cubic Dirac equation
Abstract: We outline recent work towards a global well-posedness theory for the massless cubic Dirac equation for small, scale invariant data in spatial dimensions n = 2, 3. The main difficulty is the lack of available Strichartz estimates for the Dirac equation in low dimensions. To overcome this, there are two main steps. The first is a construction of the null frame spaces of Tataru that is adapted to the Dirac equation, and which form a suitable replacement for certain missing endpoint Strichartz estimates. The second is a number of bilinear and trilinear estimates that exploit subtle cancellations in the structure of the cubic non-linearity. This is joint work with Nikolaos Bournaveas.
Title: Critical well-posedness for the Cubic Dirac equation
Abstract: We outline recent work towards a global well-posedness theory for the massless cubic Dirac equation for small, scale invariant data in spatial dimensions n = 2, 3. The main difficulty is the lack of available Strichartz estimates for the Dirac equation in low dimensions. To overcome this, there are two main steps. The first is a construction of the null frame spaces of Tataru that is adapted to the Dirac equation, and which form a suitable replacement for certain missing endpoint Strichartz estimates. The second is a number of bilinear and trilinear estimates that exploit subtle cancellations in the structure of the cubic non-linearity. This is joint work with Nikolaos Bournaveas.
28.08.2014