A new family of exact solutions to the unsteady Navier–Stokes equations using canonical transformation with complex coefficients

This paper aims to show a new family of exact solutions to the unsteady Navier–Stokes equations by using the canonical transformation with complex coefficients. This transformation transforms the system of non-linear partial differential equations to a linear system of partial differential equations...

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Bibliographic Details
Published in:Applied mathematics and computation 2008-02, Vol.196 (1), p.303-308
Main Author: Al-Mdallal, Qasem M.
Format: Article
Language:English
Subjects:
Algebra
Algebraic geometry
Exact sciences and technology
Mathematical analysis
Mathematics
Navier–Stokes equations
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
Separation of variables
System of non-linear partial differential equations
Wave variable
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Summary:This paper aims to show a new family of exact solutions to the unsteady Navier–Stokes equations by using the canonical transformation with complex coefficients. This transformation transforms the system of non-linear partial differential equations to a linear system of partial differential equations with less independent variables. The present results demonstrate that the general real solutions may involve either exp, sin, cos, sinh or cosh under certain conditions depending on the type of the constants in the canonical transformation.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2007.05.054