Abstract
Publisher Summary A kinematical symmetry of an equation is a coordinate transformation that leaves this equation invariant. Examples of kinematical symmetries are provided by the Galilei or Poincare invariance of the free particle wave equations of nonrelativistic or relativistic quantum mechanics. The largest kinematical symmetry group is larger than the Galilei or Poincare group, as in the case of the conformal group for the Maxwell equations or the Schrodinger group for the free Schrodinger equation or the diffusion equation. This chapter presents the application of the notion of kinematical symmetry to nonlinear equations, namely, to the Navier–Stokes (NS) equation of hydrodynamics. The chapter also explains the determination of the largest kinematical symmetry group of the NS equation up to a stage where a decision has to be taken on the permitted transformation behavior of pressure.
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