On asymptotically almost periodic mild solutions for Navier-Stokes equations on non-compact Riemannian manifolds
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909384499527680 |
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| author | Xuan, Pham Truong Van, Nguyen Thi |
| author_facet | Xuan, Pham Truong Van, Nguyen Thi |
| contents | In this paper, we study the existence, uniqueness and asymptotic behaviour of almost periodic and asymptotically almost periodic mild solutions to the incompressible Navier-Stokes equations on $d$-dimensional non-compact manifold $(\mathcal{M},g)$ which satisfies some bounded conditions on curvature tensors. First, we use the $L^p-L^q$-dipsersive and smoothing estimates of the Stokes semigroup to prove Massera-type principles which guarantees the well-posedness of almost periodic and asymptotically almost periodic mild solutions for the inhomogeneous Stokes equations. Then, by using fixed point arguments and Gronwall's inequality we establish the well-posedness and exponential decay for global-in-time of such solutions of Navier-Stokes equations. Our results extend the previous ones \cite{Xuan2022,Xuan2023} to the generalized non-compact Riemannian manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_14137 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On asymptotically almost periodic mild solutions for Navier-Stokes equations on non-compact Riemannian manifolds Xuan, Pham Truong Van, Nguyen Thi Analysis of PDEs Mathematical Physics Differential Geometry Dynamical Systems Functional Analysis In this paper, we study the existence, uniqueness and asymptotic behaviour of almost periodic and asymptotically almost periodic mild solutions to the incompressible Navier-Stokes equations on $d$-dimensional non-compact manifold $(\mathcal{M},g)$ which satisfies some bounded conditions on curvature tensors. First, we use the $L^p-L^q$-dipsersive and smoothing estimates of the Stokes semigroup to prove Massera-type principles which guarantees the well-posedness of almost periodic and asymptotically almost periodic mild solutions for the inhomogeneous Stokes equations. Then, by using fixed point arguments and Gronwall's inequality we establish the well-posedness and exponential decay for global-in-time of such solutions of Navier-Stokes equations. Our results extend the previous ones \cite{Xuan2022,Xuan2023} to the generalized non-compact Riemannian manifolds. |
| title | On asymptotically almost periodic mild solutions for Navier-Stokes equations on non-compact Riemannian manifolds |
| topic | Analysis of PDEs Mathematical Physics Differential Geometry Dynamical Systems Functional Analysis |
| url | https://arxiv.org/abs/2304.14137 |