Relative energy method for weak–strong uniqueness of the inhomogeneous Navier–Stokes equations far from vacuum

Crin-Barat T, Skondrić S, Violini A (2025)

Publication Language: English

Publication Type: Journal article

Publication year: 2025

Journal

Journal of Evolution Equations Springer Verlag (Germany)

Book Volume: 25

Article Number: 6

Journal Issue: 1

DOI: 10.1007/s00028-024-01036-8

Abstract

We present a weak–strong uniqueness result for the inhomogeneous Navier–Stokes equations in ℝd (d=2,3) for bounded initial densities that are far from vacuum. Given a strong solution, i.e. a solution satisfying the equation as an identity in L2, and a Leray–Hopf weak solution, we establish that they coincide if the initial data agree. Our proof strategy is based on the relative energy method and new W-1,p-type stability estimates for the density. A key point lies in proving that every Leray–Hopf weak solution originating from initial densities far from vacuum remains distant from vacuum at all times.

Authors with CRIS profile

Timothée Crin-Barat
Stefan Skondrić Lehrstuhl für Analysis

Involved external institutions

Toulouse Mathematics Institute / Institut de Mathématiques de Toulouse (IMT) FR France (FR) Universität Basel CH Switzerland (CH)

How to cite

APA:

Crin-Barat, T., Skondrić, S., & Violini, A. (2025). Relative energy method for weak–strong uniqueness of the inhomogeneous Navier–Stokes equations far from vacuum. Journal of Evolution Equations, 25(1). https://doi.org/10.1007/s00028-024-01036-8

MLA:

Crin-Barat, Timothée, Stefan Skondrić, and Alessandro Violini. "Relative energy method for weak–strong uniqueness of the inhomogeneous Navier–Stokes equations far from vacuum." Journal of Evolution Equations 25.1 (2025).

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