Characteristic Initial Value Problem for Spherically Symmetric Barotropic Flow

TL;DR

This paper analyzes the equations governing spherically symmetric barotropic fluid flow, demonstrating global solvability of constraints and local existence and uniqueness of smooth solutions given intersecting characteristic data.

Contribution

It introduces a method to solve the constraint equations globally and proves local existence and uniqueness of solutions from intersecting characteristic data.

Findings

Constraint equations can be solved globally away from the center.

Existence and uniqueness of smooth solutions are established locally.

The approach uses Riemann invariants and characteristic form.

Abstract

We study the equations of motion for a barotropic fluid in spherical symmetric flow. Making use of the Riemann invariants we consider the characteristic form of these equations. In a first part, we show that the resulting constraint equations along characteristics can be solved globally away from the center of symmetry. In a second part, given data on two intersecting characteristics, we show existence and uniqueness of a smooth solution in a neighborhood in the future of these characteristics.