SOLUTION FORMULA FOR THE VORTICITY EQUATIONS IN THE HALF PLANE WITH APPLICATION TO HIGH VORTICITY CREATION AT ZERO VISCOSITY LIMIT

作者：Maekawa Yasunori^*

来源：Advances in Differential Equations, 2013, 18(1-2): 101-146.

We consider the Navier-Stokes equations for viscous incompressible flows in the half plane under the no-slip boundary condition. In this paper we first establish a solution formula for the vorticity equations through the appropriate vorticity formulation. The formula is then applied to establish the asymptotic expansion of vorticity fields at nu -%26gt; 0 that holds at least up to the time c nu(1/3), where nu is the viscosity coefficient and c is a constant. As a consequence, we get a natural sufficient condition on the initial data for the vorticity to blow up at the inviscid limit, together with explicit estimates.

• 出版日期2013-2