Tim Candy (Imperial College)
Critical well-posedness for the Cubic Dirac equation
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 the null structure
of the equation.