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

Leandro Lichtenfelz

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arXiv · 1502.06269

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

Leandro Lichtenfelz

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Abstract

In a well-known work, M. Anderson constructed a Hadamard manifold $(M^n, g)$ which carries non-zero $L^2$ harmonic $p$-forms when $p \neq n/2$, thus disproving the Dodziuk-Singer conjecture. In this paper, we use the manifold $(M^3, g)$ in order to solve another problem in geometric analysis, namely the nonuniqueness of solutions of Leray-Hopf type of the Navier-Stokes equations.

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BibTeX RIS

Leandro Lichtenfelz. 2015-02-22. Nonuniqueness of solutions of the Navier-Stokes equations on negatively curved Riemannian manifolds. https://arxiv.org/abs/1502.06269

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