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.
CitationYuen, 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
- Euler equations
- Exact solutions
- Symmetry reductions
- Navier–Stokes equations