How and why non smooth solutions of the 3D Navier-Stokes equations could possibly develop

Funaro Daniele

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How and why non smooth solutions of the 3D Navier-Stokes equations could possibly develop

机译：3D Navier-Stokes 方程的非光滑解如何以及为什么可能发展

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Fluid configurations in three-dimensions, displaying a plausible decay of regularity in a finite time, are suitably built and examined. Vortex rings are the primary ingredients in this study. The full Navier-Stokes system is converted into a 3D scalar problem, where appropriate numerical methods are implemented in order to figure out the behavior of the solutions. Further simplifications in 2D and 1D provide interesting toy problems, that may be used as a starting platform for a better understanding of blowup phenomena.

机译：三维流体构型在有限的时间内显示出合理的规律性衰减，被适当地构建和检查。涡环是本研究的主要成分。将完整的 Navier-Stokes 系统转换为 3D 标量问题，其中实施了适当的数值方法以找出解的行为。2D 和 1D 的进一步简化提供了有趣的玩具问题，可以用作更好地理解爆炸现象的起始平台。

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来源
《Numerische Mathematik》 |2022年第4期|789-817|共29页
作者
Funaro Daniele;
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作者单位

Univ Modena & Reggio Emilia;

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原文格式 PDF
正文语种英语
中图分类数值分析;
关键词
35Q30; 76N10; WEAK SOLUTIONS; PARTIAL REGULARITY; SINGULARITY; ENERGY; BLOW;

机译：35Q30;76N10;弱解决方案;偏正则性;奇点;能源;吹;

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1. Exponential Decay and Regularity of Global Solutions for the 3D Navier-Stokes Equations Posed on Lipschitz and Smooth Domains [J] . Larkin N. A., Padilha M. V. Journal of mathematical fluid mechanics . 2020,第3期

机译：Exponential Decay and Regularity of Global Solutions for the 3D Navier-Stokes Equations Posed on Lipschitz and Smooth Domains
2. Smooth solution for incompressible Navier-Stokes equations with large initial [J] . Li Rulv Applicable Analysis . 2023,第10期

机译：Smooth solution for incompressible Navier-Stokes equations with large initial
3. Global Smooth Solutions to the 2-D Nonhomogeneous Navier-Stokes Equations [J] . Ping Zhang International mathematics research notices: IMRN . 2008,第22期

机译：Global Smooth Solutions to the 2-D Nonhomogeneous Navier-Stokes Equations
4. 带内部阻尼的拟线性梁六程的局部光滑解（Local Smooth Solutions for a Quasi-linear Beam with Distributed Damping） [C] . Chinese Control Conference vol.2; 20040810-13; Wuxi(CN) . 2004

机译：带内部阻尼的拟线性梁六程的局部光滑解（Local Smooth Solutions for a Quasi-linear Beam with Distributed Damping）
5. Avoiding singularity formation in the 3-D Navier-Stokes flows. [D] . Guberovic, Rafaela. 2009

机译：避免在3D Navier-Stokes流中形成奇异点。
6. A Numerical Method for Solving the 3D Unsteady Incompressible Navier-Stokes Equations in Curvilinear Domains with Complex Immersed Boundaries [O] . Liang Ge, Fotis Sotiropoulos -1

机译：具有复杂浸入边界的曲线域中求解3D非稳态不可压缩Navier-Stokes方程的数值方法
7. Un exemple de feuilletage modulaire d\'eduit d'une solution alg\'ebrique de l'\'equation de Painlev\'e VI [O] . Cousin, Gaël 2013

机译：例如，de e feuilletage modulaire d \'eduit d'une solution alg \'ebrique de l'\'equation de painlev \'e VI
8. Criterion for Approximating Time-Periodic Solutions to the Navier-StokesEquations (Critere pour l'Approximation des Solutions Periodiques des Equations de Navier-Stokes) [R] . Titi, E. S. 1991

机译：用于逼近Navier-stokes方程的时间周期解的判据（Critere pour l'ofimation des solutions periodiques des Equations de Navier-stokes）

How and why non smooth solutions of the 3D Navier-Stokes equations could possibly develop

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