On the well-posedness of a 2D nonlinear and nonlocal system arising from   the dislocation dynamics
  In this paper we consider a 2D nonlinear and nonlocal model describing the dynamics of the dislocation densities. We prove the local well-posedness of strong solution to this system in the suitable functional framework, and we show the global well-posedness for some dissipative cases by the method of nonlocal maximum principle. 
Dong Li, Changxing Miao and Liutang Xue
math.AP math-ph math.MP