LOCAL WELL-POSEDNESS FOR THE NONLINEAR DIRAC EQUATION IN TWO SPACE DIMENSIONS

作者：Pecher Hartmut^*

来源：Communications on Pure and Applied Analysis, 2014, 13(2): 673-685.

DOI：10.3934/cpaa.2014.13.673

• Dirac equation
• well-posedness
• Fourier restriction norm method

The Cauchy problem for the cubic nonlinear Dirac equation in two space dimensions is locally well-posed for data in H-s for s > 1/2. The proof given in spaces of Bourgain-Klainerman-Machedon type relies on the null structure of the nonlinearity as used by d'Ancona-Foschi-Selberg for the Dirac-Klein-Gordon system before and bilinear Strichartz type estimates for the wave equation by Selberg and Foschi-Klainerman.

• 出版日期2014-3