Semi-invariant solutions of the Navier-Stokes equations

V. Rosenhaus, Ravi Shankar, Cody Squellati

Research output: Contribution to journalArticlepeer-review


We present new exact solutions and reduced differential systems of the Navier-Stokes equations of incompressible viscous fluid flow. We apply the method of semi-invariant manifolds, introduced earlier as a modification of the Lie invariance method. We show that many known solutions of the Navier-Stokes equations are, in fact, semi-invariant and that the reduced differential systems we derive using semi-invariant manifolds generalize previously obtained results that used ad hoc methods. Many of our semi-invariant solutions solve decoupled systems in triangular form that are effectively linear. We also obtain several new reductions of Navier-Stokes to a single nonlinear partial differential equation. In some cases, we can solve reduced systems and generate new analytic solutions of the Navier-Stokes equations or find their approximations, and physical interpretation.

Original languageEnglish (US)
Pages (from-to)2853-2893
Number of pages41
JournalMathematical Methods in the Applied Sciences
Issue number8
StatePublished - May 30 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • General Engineering


  • Euler equations
  • Navier-Stokes equations
  • analytical solutions
  • incompressible flow
  • symmetries


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