The dynamical ${\Phi }_3^4$ model by an approximation of Laplacian

Abstract

The dynamical ${\Phi }_3^4$ equation is a singular SPDE and has important applications in physics. In this paper, we consider the equation by approximating the Laplacian instead of the noise or the cubic term as in previous studies. By using a good transformation as in [JP21], we show that the approximating equation is locally well-posed and that its solution converges to the solution of the dynamical ${\Phi }_3^4$ equation. We expect to be able to show the global well-posedness and the existence of the invariant measure.

50 pages