Strong trajectory and global $\mathbf{W^{1,p}}$-attractors for the damped-driven Euler system in $\mathbb R^2$

V. V. Chepyzhov; A. A. Ilyin; S. V. Zelik

Strong trajectory and global $\mathbf{W^{1,p}}$-attractors for the damped-driven Euler system in $\mathbb R^2$

Analysis of PDEs 2015-11-13 v1

Authors: V. V. Chepyzhov , A. A. Ilyin , S. V. Zelik

Abstract

We consider the damped and driven two-dimensional Euler equations in the plane with weak solutions having finite energy and enstrophy. We show that these (possibly non-unique) solutions satisfy the energy and enstrophy equality. It is shown that this system has a strong global and a strong trajectory attractor in the Sobolev space $H^1$ . A similar result on the strong attraction holds in the spaces $H^1\cap\{u:\ \|\mathrm{curl} u\|_{L^p}<\infty\}$ for $p\ge2$ .

Keywords

damped-driven Euler equations weak solutions energy equality enstrophy equality strong global attractor strong trajectory attractor Sobolev space W^{1,p}-attractors

Cite

@article{arxiv.1511.03873,
  title  = {Strong trajectory and global $\mathbf{W^{1,p}}$-attractors for the damped-driven Euler system in $\mathbb R^2$},
  author = {V. V. Chepyzhov and A. A. Ilyin and S. V. Zelik},
  journal= {arXiv preprint arXiv:1511.03873},
  year   = {2015}
}

Strong trajectory and global $\mathbf{W^{1,p}}$-attractors for the damped-driven Euler system in $\mathbb R^2$

Abstract

Keywords

Cite

Related papers