English

Damped Infinite Energy Solutions of the 3D Euler and Boussinesq Equations

Analysis of PDEs 2016-07-01 v3 Mathematical Physics math.MP

Abstract

We revisit a family of infinite-energy solutions of the 3D incompressible Euler equations proposed by Gibbon et al. [9] and shown to blowup in finite time by Constantin [6]. By adding a damping term to the momentum equation we examine how the damping coefficient can arrest this blowup. Further, we show that similar infinite-energy solutions of the inviscid 3D Boussinesq system with damping can develop a singularity in finite time as long as the damping effects are insufficient to arrest the (undamped) 3D Euler blowup in the associated damped 3D Euler system.

Keywords

Cite

@article{arxiv.1605.08965,
  title  = {Damped Infinite Energy Solutions of the 3D Euler and Boussinesq Equations},
  author = {William Chen and Alejandro Sarria},
  journal= {arXiv preprint arXiv:1605.08965},
  year   = {2016}
}

Comments

14 pages; some typos have been corrected