تقرير
Large time behavior of solutions to the $3$D anisotropic Navier-Stokes equation
| العنوان: | Large time behavior of solutions to the $3$D anisotropic Navier-Stokes equation |
|---|---|
| المؤلفون: | Fujii, MIkihiro |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, 35Q30, 35B40, 35Q35 |
| الوصف: | We consider the large time behavior of the solution to the $3$D Navier-Stokes equation with horizontal viscosity $\Delta_{\rm h} u=\partial_1^2 u+\partial_2^2 u$ and show that the $L^p$ decay rate of the horizontal components of the velocity field coinsides to that of the $2$D heat kernel, while the vertical component decays like the $3$D heat kernel. Moreover, we consider the asymptotic expansion of the solution and find that a portion of the nonlinear term affect the leading term of the horizontal components of the velocity field, whereas the leading term of the vertical component is given by only the linear solution. Comment: 27 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2108.11940 |
| رقم الأكسشن: | edsarx.2108.11940 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |