Work

Inhomogeneous 2D Navier–Stokes Equations: Existence, Uniqueness, Stability, Continuity in Time and Energy Conservation of Weak Solutions

Year: 2026

Type: article

Abstract: We present a novel and direct proof of the existence and uniqueness of weak solutions of the inhomogeneous incompressible Navier–Stokes equations without vacuum. The analysis we employ to prove the strong convergence of the approximating sequence, which is based on the relative energy method, reveals how to conclude the stability and uniqueness of weak solutions. To the best of our knowledge, these global-in-time stability estimates are completely new. Furthermore, for the first time, we establish energy conservation for weak solutions.

Source: Journal of Mathematical Fluid Mechanics

DOI: 10.1007/s00021-026-01052-3

Author: Stefan Škondrić

Institution: Friedrich-Alexander-Universität Erlangen-Nürnberg

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,390

Funders: Institut de Mathématiques de Toulouse, Deutsche Forschungsgemeinschaft, Centre International de Mathématiques et Informatique de Toulouse