Viscous approximations and decay rate of maximal vorticity function for 3D axisymmetric Euler equations
The paper deals with the axially symmetric motion of incompressible homogeneous inviscid flows. In this case we arrive at 3D axially symmetric Euler equations without swirls. It is proved that the viscous approximations, which are the solutions of the corresponding Navier-Stokes equations with the initial data converge strongly in \(L^2([0,T];L^2_{\text{loc}} (\mathbb R^3))\) provided that they have strong convergence in the region away from the symmetry axis. A sufficient condition to guarantee the strong convergence in the region away from the symmetry axis is given. The decay rate of the vorticity maximal function is also investigated.
scientific article; zbMATH DE number 2104897