Local existence and uniqueness for the frictional Newton-Schroedinger equation in three dimensions

TL;DR

This paper establishes local existence and uniqueness results for the three-dimensional frictional Newton-Schroedinger equation, demonstrating the solution's continuous dependence on initial data and the blow-up alternative.

Contribution

It provides the first proof of local well-posedness and blow-up criteria for the 3D frictional Newton-Schroedinger equation.

Findings

Proved local existence and uniqueness of solutions.

Established continuous dependence on initial data.

Confirmed the blow-up alternative holds true.

Abstract

We prove local existence and uniqueness for the Newton-Schroedinger equation in three dimensions. Further we show that the blow-up alternative holds true as well as the continuous dependence of the solution w.r.t. the initial data.