Similarity Reductions and Exact Solutions for the Two‐Dimensional Incompressible Navier–Stokes Equations

DOI10.1111/1467-9590.00125zbMath1136.76342OpenAlexW2044948396MaRDI QIDQ4784680

David K. Ludlow, Andrew P. Bassom, Peter A. Clarkson

Publication date: 11 December 2002

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1111/1467-9590.00125

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Nonlinear ordinary differential equations and systems (34A34) Dimensional analysis and similarity applied to problems in fluid mechanics (76M55) Navier-Stokes equations (35Q30) Solutions to PDEs in closed form (35C05)

Related Items (15)

Some analytical solutions for the advection--dispersion equation. ⋮ Direct functional separation of variables and new exact solutions to axisymmetric unsteady boundary-layer equations ⋮ Construction of exact solutions to nonlinear PDEs with delay using solutions of simpler PDEs without delay ⋮ New nonlinear systems admitting Virasoro-type symmetry algebra and group-invariant solutions ⋮ A new class of non-helical exact solutions of the Navier-Stokes equations ⋮ Explicitly self-similar solutions for the Euler/Navier-Stokes-Korteweg equations in \(R^N\) ⋮ Some similarity solutions for three-dimensional boundary layers ⋮ New classes of exact solutions and some transformations of the Navier-Stokes equations ⋮ The Cartesian Vector Solutions for the N‐Dimensional Compressible Euler Equations ⋮ One class of regular partially invariant solutions of the Navier-Stokes equations ⋮ Similarity reductions and new nonlinear exact solutions for the 2D incompressible Euler equations ⋮ Symmetry transformation of solutions for the Navier-Stokes equations ⋮ Exact solutions to generalized plane Beltrami--Trkal and Ballabh flows ⋮ Vortices and invariant surfaces generated by symmetries for the 3D Navier-Stokes equations ⋮ Exact solutions of unsteady three-dimensional Navier-Stokes equations

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