AN ELEMENTARY APPROACH TO THE 3D NAVIER-STOKES EQUATIONS WITH NAVIER BOUNDARY CONDITIONS: EXISTENCE AND UNIQUENESS OF VARIOUS CLASSES OF SOLUTIONS IN THE FLAT BOUNDARY CASE

Luigi C. Berselli

首页> 外文期刊>Discrete and continuous dynamical systems▼hSeries S >AN ELEMENTARY APPROACH TO THE 3D NAVIER-STOKES EQUATIONS WITH NAVIER BOUNDARY CONDITIONS: EXISTENCE AND UNIQUENESS OF VARIOUS CLASSES OF SOLUTIONS IN THE FLAT BOUNDARY CASE

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AN ELEMENTARY APPROACH TO THE 3D NAVIER-STOKES EQUATIONS WITH NAVIER BOUNDARY CONDITIONS: EXISTENCE AND UNIQUENESS OF VARIOUS CLASSES OF SOLUTIONS IN THE FLAT BOUNDARY CASE

机译：具有Navier边界条件的3D Navier-Stokes方程的基本方法：平面边界情况下各种类解的存在和唯一性

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Dedicated to V. A. Solonnikov on the occasion of his 75th birthdayrnWe study with elementary tools the stationary 3D Navier-Stokes equations in a flat domain, equipped with Navier (slip without friction) boundary conditions. We prove existence and uniqueness of weak, strong, and very-weak solutions in appropriate Banach spaces and most of the result hold true without restrictions on the size of the data. Results are partially known, but our approach allows us to give rather elementary and self-contained proofs.

机译：在V. A. Solonnikov诞辰75周年之际，我们用基本工具研究了平面域中固定的3D Navier-Stokes方程，该方程配备了Navier（无摩擦滑移）边界条件。我们证明了在适当的Banach空间中弱，强和非常弱的解决方案的存在和唯一性，并且大多数结果成立，而对数据大小没有限制。结果是部分已知的，但是我们的方法使我们能够提供相当基本且独立的证明。

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《Discrete and continuous dynamical systems▼hSeries S》 |2010年第2期|P.199-219|共21页
作者
Luigi C. Berselli;
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作者单位

Dipartimento di Matematica Applicata 'U. Dini' Via F. Buonarroti 1/c I-56127, Pisa, Italy;

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正文语种 eng
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stokes and navier-stokes equations; navier's boundary conditions; L~q-theory; very-weak solutions;

机译：斯托克斯和纳斯托斯方程;航海者的边界条件;L〜q理论非常弱的解决方案;

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1. An elementary approach to the inviscid limits for the 3D Navier-Stokes equations with slip boundary conditions and applications to the 3D Boussinesq equations [J] . Luigi C. Berselli, Stefano Spirito Nonlinear differential equations and applications: NoDEA . 2014,第2期

机译：带滑移边界条件的3D Navier-Stokes方程无粘极限的基本方法及其在3D Boussinesq方程中的应用
2. Global existence and uniqueness of solutions to the initial boundary value problem of 3D Navier-Stokes equations with Cattaneo law [J] . Qin Yuming, Lv Gaofeng Applied mathematics letters . 2020,第期

机译：Cattaneo法律3D Navier-Stokes方程初立边值问题解决方案的全球存在与唯一性
3. On a two components condition for regularity of the 3D Navier-Stokes equations under physical slip boundary conditions on non-flat boundaries [J] . de Veiga Hugo Beirao, Bemelmans Josef, Brand Johannes Mathematische Annalen . 2019,第3a4期

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4. Question of Existence and Uniqueness of Solution for Navier-Stokes Equation with Linear "Do-Nothing" Type Boundary Condition on the Outflow [C] . Tomas Neustupa International Conference on Numerical Analysis and Its Applications . 2009

机译：Navier-Stokes方程解决方案的存在性和唯一性，用线性“无”型边界条件对外流
5. The influence of surface perturbations and laminar separation bubble on boundary layer instability by direct numerical solution of the Navier-Stokes equations. [D] . Elli, Shahram. 1992

机译：通过Navier-Stokes方程的直接数值解，表面扰动和层流分离气泡对边界层不稳定性的影响。
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. An elementary approach to the 3D Navier-Stokes equations with Navier boundary conditions: Existence and uniqueness of various classes of solutions in the flat boundary case [O] . BERSELLI L.C. 2010

机译：3D基本方法具有Navier边界条件的Navier-Stokes方程：存在公寓中各种解决方案的独特性边界情况
8. On the Existence of Solutions of the Steady-State Navier-Stokes Equations for a Class of Non-Smooth Boundary Data [R] . Edwards, J. E. 1963

机译：一类非光滑边界数据的稳态Navier-stokes方程解的存在性

AN ELEMENTARY APPROACH TO THE 3D NAVIER-STOKES EQUATIONS WITH NAVIER BOUNDARY CONDITIONS: EXISTENCE AND UNIQUENESS OF VARIOUS CLASSES OF SOLUTIONS IN THE FLAT BOUNDARY CASE

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