Fundamental solutions for steady, three‑dimensional magnetohydrodynamic flow past a point source
This work develops a fundamental disturbance solution for a complex, non‑dissipative fluid governed by Lundquist equations, blending elliptic and hyperbolic features to describe the flow field created by a point source.
The study examines small, steady disturbances in an isentropic, perfectly conducting fluid with constant velocity, density, and magnetic field. By extending plane wave methods and introducing smoothing techniques, the author derives a fundamental solution that satisfies specific causality and decay conditions. The approach separates the transverse and compressive parts of the flow, then builds the solution through a series of careful mathematical steps that ensure smoothness across critical surfaces while preserving the expected singular behavior along real characteristic directions.
- How steady, three‑dimensional magnetohydrodynamic flow is modeled with Lundquist equations
- How plane waves with complex speeds are used to construct the fundamental solution
- How a smoothing function is added to enforce continuity across z = 0
- How causality and decay requirements shape the final solution
Ideal for readers of advanced fluid dynamics and plasma physics who seek a rigorous, distribution‑level description of disturbances from a point source in a non‑dissipative MHD setting.