Local Well‐Posedness for Nonlinear Dirac Equation on N ‐Star Metric Graphs

ABSTRACT

We consider the Cauchy problem for the nonlinear Dirac equation on a noncompact ‐star metric graph , where , , and denotes the self‐adjoint Dirac–Kirchhoff operator on . Using Bourgain‐type spaces defined through the spectral resolution of , together with elementary bounds for the Dirac flow and fractional Nemytskii estimates below the trace threshold, we prove local well‐posedness for initial data The corresponding solution belongs to Moreover, is conserved along the solution on the existence interval. We also establish a blow‐up alternative in the combined and space–time control norm.