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arXiv · 2101.03306

On asymptotically almost periodic solutions to the Navier-Stokes equations on hyperbolic manifolds

Pham Truong Xuan·Nguyen Thi Van
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Abstract

In this paper we study the forward asymptotically almost periodic (AAP-) mild solutions of Navier-Stokes equations on the real hyperbolic manifold $\mathcal{M}=\mathbb{H}^d(\mathbb{R})$ with dimension $d \geq 2$. Using the dispersive and smoothing estimates for the Stokes equation we invoke the Massera-type principle to prove the existence and uniqueness of the AAP- mild solution for the inhomogeneous Stokes equations in $L^p(\Gamma(T\mathcal{M})))$ space with $1 1$.

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BibTeXRIS

Pham Truong Xuan, Nguyen Thi Van. 2021-01-09. On asymptotically almost periodic solutions to the Navier-Stokes equations on hyperbolic manifolds. https://doi.org/10.1007/s11784-023-01074-8

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