تقرير
Navier-Stokes equations in a curved thin domain, Part III: thin-film limit
| العنوان: | Navier-Stokes equations in a curved thin domain, Part III: thin-film limit |
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| المؤلفون: | Miura, Tatsu-Hiko |
| المصدر: | Adv. Differential Equations 25 (2020), no. 9/10, 457-626 |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, Primary: 35B25, 35Q30, 76D05, Secondary: 35R01, 76A20 |
| الوصف: | We consider the Navier-Stokes equations with Navier's slip boundary conditions in a three-dimensional curved thin domain around a given closed surface. Under suitable assumptions we show that the average in the thin direction of a strong solution to the bulk Navier-Stokes equations converges weakly in appropriate function spaces on the limit surface as the thickness of the thin domain tends to zero. Moreover, we characterize the limit as a weak solution to limit equations, which are the damped and weighted Navier-Stokes equations on the limit surface. We also prove the strong convergence of the average of a strong solution to the bulk equations towards a weak solution to the limit equations by showing estimates for the difference between them. In some special case our limit equations agree with the Navier-Stokes equations on a Riemannian manifold in which the viscous term contains the Ricci curvature. This is the first result on a rigorous derivation of the surface Navier-Stokes equations on a general closed surface by the thin-film limit. Comment: 122 pages, typos corrected, references updated. This paper is the last part of the divided and revised version of arXiv:1811.09816 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2002.06350 |
| رقم الأكسشن: | edsarx.2002.06350 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |