One dimensional Dirac equation with quadratic nonlinearities
One dimensional Dirac equation with quadratic nonlinearities
The local well-posedness for the nonlinear Dirac equation with special forms of quadratic nonlinearities in one space dimension is obtained by two approaches. One is to apply the Fourier restriction norm method of Bourgain [2, 3] by showing the bilinear estimates for the nonlinearities. Another is to study the explicit …