Energy decay for a weak solution of the Navier-Stokes equation with slowly varying external forces (Q676194)

Under some suitable conditions on the external forces and initial velocity, the authors construct a weak solution to the Navier-Stokes equations and demonstrate that the solution satisfies a generalized energy inequality. Using this inequality and the Fourier splitting method, the authors show that the energy norm of the weak solution has a non-uniform decay. For external forces with a given explicit decay rate, they demonstrate that the energy has a uniform rate of decay.