Finite time blowup and global solutions of Euler type equations in matrix geometry

Abstract

In an interesting recent work, Professor Sullivan has proposed a matrix version of the Euler equation to approach this problem from a new angle. Motivated by his work, we consider the finite time blowup and global solutions of Euler type equations in the matrix geometry. We set up some invariant sets of the flow equations, and the invariant sets are defined via the use of the free energy functional and the Nehari functional in the matrix geometry model. The blowup result is obtained by the convexity method.