A (3+1)-dimensional equation of plasma drift waves perturbed by a singular potential in an infinite parallelepiped

Abstract

We investigate the existence and nonexistence of weak solutions to a (3+1)-dimensional equation of plasma drift waves perturbed by a singular potential. The considered equation is posed in an infinite parallelepiped, under an inhomogeneous Dirichlet boundary condition. We show that the dividing line with respect to existence or nonexistence is given by a critical exponent.