Remarks on the inviscid limit of weak solutions of the Navier–Stokes equations

The paper analyzes the inviscid limit of weak solutions to the incompressible Navier–Stokes equations within physical boundaries. We establish a sufficient regularity condition that ensures the Navier–Stokes solutions exhibit global viscous dissipation. Moreover, we prove that as the viscous coefficient tends to zero, the weak solutions converge to those of the Euler equations. We assume that the weak solutions are uniformly bounded with respect to viscosity in $L^3\left(0,T;B_3^{\alpha ,\infty }\right)$ in the interior domain, and that certain mean integral conditions in the space–time region exhibit prescribed decay rates near the boundary.