Symmetry reduction and exact solutions of the Navier-Stokes equations

Abstract

Ansatzes for the Navier-Stokes field are described. These ansatzes reduce the Navier-Stokes equations to system of differential equations in three, two, and one independent variables. The large sets of exact solutions of the Navier-Stokes equations are constructed.

LaTex2e, 62 pages

Cited by in corpus (22)

• Enhanced preliminary group classification of a class of generalized diffusion equations
• Symmetry preserving parameterization schemes
• Lie symmetries and exact solutions of the barotropic vorticity equation
• Exact Solutions of a Remarkable Fin Equation
• Lie symmetry analysis and exact solutions of the quasi-geostrophic two-layer problem
• Reduction Operators of Linear Second-Order Parabolic Equations
• Singular reduction operators in two dimensions
• Extended symmetry analysis of generalized Burgers equations
• Enhanced symmetry analysis of two-dimensional Burgers system
• Point symmetry group of the barotropic vorticity equation
• Extended symmetry analysis of two-dimensional degenerate Burgers equation
• Consequences of Symmetries on the Analysis and Construction of Turbulence Models
• Singular reduction modules of differential equations
• Lie reduction and exact solutions of vorticity equation on rotating sphere
• Conservation laws and hierarchies of potential symmetries for certain diffusion equations
• Point-symmetry pseudogroup, Lie reductions and exact solutions of Boiti-Leon-Pempinelli system
• Equivalence of Q-Conditional Symmetries under Group of Local Transformation
• Reduction operators of Burgers equation
• On the ineffectiveness of constant rotation in the primitive equations and their symmetry analysis
• Lie reductions and exact solutions of dispersionless Nizhnik equation
• Space-time decay of Navier-Stokes flows invariant under rotations
• Hidden symmetries, hidden conservation laws and exact solutions of dispersionless Nyzhnyk equation