On the nonrelativistic limit of a semilinear field equation in a uniform and isotropic space

TL;DR

This paper investigates the nonrelativistic limit of a semilinear field equation in a uniform, isotropic space, analyzing solutions, spatial effects, and dissipative properties within a mathematical physics framework.

Contribution

It constructs the space's scale-function from Einstein's equation and studies the limit-equation's solutions, including global and blow-up behaviors, considering spatial variance effects.

Findings

Global solutions are established in Sobolev spaces.

Blow-up solutions are characterized under certain conditions.

Dissipative properties of the limit-equation are identified.

Abstract

The nonrelativistic limit of a semilinear field equation is considered in a uniform and isotropic space.The scale-function of the space is constructed based on the Einstein equation.The Cauchy problem of the limit-equation is considered,and global and blow-up solutions are shown in Sobolev spaces. The role of spatial variance on the problem is studied,and some dissipative properties of the limit-equation are remarked.