New Class of Exact Solutions of Navier-Stokes Equations with Exponential Dependence of Velocity on Two Spatial Coordinates

Prosviryakov E. Yu.

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New Class of Exact Solutions of Navier-Stokes Equations with Exponential Dependence of Velocity on Two Spatial Coordinates

机译：Navier-Stokes方程的新类精确解决方案，具有两种空间坐标对指数依赖性的指数依赖性

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A new class of exact solutions of nonlinear and linearized Navier-Stokes equations has been proposed, which generalize the well-known family of exact solutions in which the velocity is linear in some coordinates. The case of the quadratic dependence of the velocities on two horizontal (longitudinal) coordinates with coefficients that are the functions of the vertical (transverse) coordinate and time was considered in detail. The solutions were generalized for rotating liquids. Equations for constructing exact solutions with an arbitrary dependence of velocities on the horizontal coordinates were derived.

机译：已经提出了一种新的非线性和线性化Navier-Stokes方程的精确解决方案，这概括了众所周知的精确解决方案，其中速度在一些坐标中是线性的。在两个水平（纵向）坐标上具有垂直（横向）坐标和时间的函数的系数的速度对速度的二次依赖性的情况。将溶液普遍为旋转液体。衍生用于构建具有在水平坐标上的任意依赖性的精确溶液的方程。

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来源
《Theoretical foundations of chemical engineering》 |2019年第1期|107-114|共8页
作者
Prosviryakov E. Yu.;
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作者单位

Russian Acad Sci Ural Branch Inst Engn Sci Ekaterinburg 620049 Russia;

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原文格式 PDF
正文语种 eng
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关键词
exact solutions; Navier-Stokes equations; Stokes approximation; Oseen approximation; rotating liquid; counterflows;

机译：精确解决方案;Navier-Stokes方程;斯托克斯近似;Oseen近似;旋转液体;逆流;

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专利

1. New Class of Exact Solutions of Navier-Stokes Equations with Exponential Dependence of Velocity on Two Spatial Coordinates [J] . Prosviryakov E. Yu. Theoretical foundations of chemical engineering . 2019,第1期

机译：速度与两个空间坐标呈指数相关的Navier-Stokes方程的新精确解
2. A New Class of Exact Solutions to the Two-Dimensional Eikonal Equation Where the Velocity in the Medium Depends on One of the Spatial Coordinates Alone [J] . E. D. Moskalensky Numerical analysis and applications . 2018,第3期

机译：对介质中速度的二维Eikonal方程的一种新的精确解决方案取决于单独的空间坐标之一
3. Exact Solutions of the Navier-Stokes Equations with the Linear Dependence of Velocity Components on Two Space Variables [J] . S. N. Aristov, D. V. Knyazev, A. D. Polyanin Theoretical foundations of chemical engineering . 2009,第5期

机译：速度分量线性依赖于两个空间变量的Navier-Stokes方程的精确解
4. A new class of exact solutions of the Navier-Stokes equations for swirling flows in porous and rotating pipes [C] . A. Fatsis, J. Statharas, A. Panoutsopoulou, International Conference on Advances in Fluid Mechanics . 2010

机译：用于旋转管道旋转流动的Navier-Stokes方程的新一类精确解决方案
5. Self-similar solutions and large time behavior of solutions to the compressible Navier-Stokes equations. [D] . Guo, Zhenhua. 2003

机译：可压缩的Navier-Stokes方程的自相似解和解的长时间行为。
6. Method for Remote Determination of Object Coordinates in Space Based on Exact Analytical Solution of Hyperbolic Equations [O] . Vladimir Kuptsov, Vladimir Badenko, Sergei Ivanov, 2020

机译：基于双曲线方程精确分析解的空间中对象坐标的远程确定方法
7. New classes of exact solutions of three-dimensional Navier-Stokes equations [O] . Aristov, S. N., Polyanin, A. D. 2009

机译：三维Navier-stokes精确解的新类方程

New Class of Exact Solutions of Navier-Stokes Equations with Exponential Dependence of Velocity on Two Spatial Coordinates

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