Global smooth solution to the 2D Boussinesq equations with fractional dissipation

Zhuan Ye

Global smooth solution to the 2D Boussinesq equations with fractional dissipation

Analysis of PDEs 2015-10-15 v2

Authors: Zhuan Ye

Abstract

In this paper, we consider the two-dimensional (2D) incompressible Boussinesq system with fractional Laplacian dissipation and thermal diffusion. Based on the previous works and some new observations, we show that the condition $1-\alpha <\beta<\min\Big\{3-3\alpha,\,\,\frac{\alpha}{2},\,\, \frac{3\alpha^{2}+4\alpha-4}{8(1-\alpha)}\Big\}$ with $0.7351\approx\frac{10-2\sqrt{10}}{5}<\alpha<1$ suffices in order for the solution pair of velocity and temperature to remain smooth for all time.

Keywords

Boussinesq equations fractional dissipation global smooth solution incompressible flow partial differential equations

Cite

@article{arxiv.1510.03237,
  title  = {Global smooth solution to the 2D Boussinesq equations with fractional dissipation},
  author = {Zhuan Ye},
  journal= {arXiv preprint arXiv:1510.03237},
  year   = {2015}
}

Comments

19 pages. This version adds some details and makes some changes. arXiv admin note: text overlap with arXiv:1506.08993

Global smooth solution to the 2D Boussinesq equations with fractional dissipation

Abstract

Keywords

Cite

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