On the blow-up of solutions of the 3-D Euler equations in a bounded domain
A problem with the Euler equations for incompressible flow is that it is not known whether its smooth solution persists for all time or it turns to be singular at some later time. It is believed that it should become singular as a result of the development of turbulence in the flow. In the present paper, it is shown that if \((0,T)\) is the maximal interval of existence for such a solution on a bounded domain, then the integral of the \(L\)-infinite norm of its vorticity over this domain is infinite. The proof of this result is based on the application of the theory of linear elliptic systems of partial differential equations to a certain elliptic system associated with Euler equations.
scientific article; zbMATH DE number 459102
scientific article