Exact, rotational, infinite energy, blowup solutions to the 3-dimensional Euler equations

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13 Citations (Scopus)

Abstract

In this Letter, we construct a new class of blowup or global solutions with elementary functions to the 3-dimensional compressible or incompressible Euler and Navier-Stokes equations. And the corresponding blowup or global solutions for the incompressible Euler and Naiver-Stokes equations are also given. Our constructed solutions are similar to the famous Arnold-Beltrami-Childress (ABC) flow. The obtained solutions with infinite energy can exhibit the interesting behaviors locally. Furthermore, due to divu→=0 for the solutions, the solutions also work for the 3-dimensional incompressible Euler and Navier-Stokes equations. Copyright © 2011 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)3107-3113
JournalPhysics Letters A
Volume375
Issue number35
DOIs
Publication statusPublished - Aug 2011

Citation

Yuen, M. (2011). Exact, rotational, infinite energy, blowup solutions to the 3-dimensional Euler equations. Physics Letters A, 375(35), 3107-3113. doi: 10.1016/j.physleta.2011.06.067

Keywords

  • Euler equations
  • Exact solutions
  • Rotational
  • Symmetry reductions
  • Blowup
  • Navier–Stokes equations

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