Implementation of the Lagrange-Galerkin methods for the incompressible Navier-Stokes equations

Abstract

In a real scalar field model in 1+1 dimensions with quartic and sextic selfcoupling there appears a classically unstable nontopological soliton which is a bubble in the false vacuum. We show that this vacuum is rendered stable by one and two-loop quantum corrections w ith appropriate renormalization conditions.