Theoretical Foundations of Chemical Engineering

, Volume 53, Issue 1, pp 107–114 | Cite as

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

  • E. Yu. ProsviryakovEmail author


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.


exact solutions Navier–Stokes equations Stokes approximation Oseen approximation rotating liquid counterflows 



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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Institute of Engineering Science, Ural Branch, Russian Academy of SciencesYekaterinburgRussia

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