Nonuniqueness of solutions of the Navier-Stokes equations on negatively curved Riemannian manifolds

2015/02/22 by Leandro Lichtenfelz, Lichtenfelz, Leandro
Computer Science · Mathematics · #32Q05 (Secondary) #76D05 (Primary) #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1502.06269

openalex publication_date 2015/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a well-known work, M. Anderson constructed a Hadamard manifold (Mⁿ, g) which carries non-zero L² harmonic p-forms when p ≠ n/2, thus disproving the Dodziuk-Singer conjecture. In this paper, we use the manifold (M³, g) in order to solve another problem in geometric analysis, namely the nonuniqueness of solutions of Leray-Hopf type of the Navier-Stokes equations.

Citations

• Sur le mouvement d'un liquide visqueux emplissant l'espace

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