On the Global Unique Solvability of Initial-Boundary Value Problems for the Coupled Modified Navier–Stokes and Maxwell Equations

摘要

The global unique solvability of the first initial-boundary value problem in a bounded, two or three-dimensional domain with fixed perfectly conducting boundaries is proved for the modified Navier–Stokes equations coupled with the Maxwell equations. The system gives a deterministic description of the dynamics for conducting, incompressible, homogeneous fluids. Improved results are proved for the periodic boundary condition case.