The Euler equations in planar nonsmooth convex domains

@article{Bardos2013TheEE,
  title={The Euler equations in planar nonsmooth convex domains},
  author={Claude W. Bardos and Francesco Di Plinio and Roger Temam},
  journal={Journal of Mathematical Analysis and Applications},
  year={2013},
  volume={407},
  pages={69-89}
}
Abstract As a model problem for the barotropic mode of the primitive equations of the oceans and atmosphere, we consider the Euler system on a bounded convex planar domain Ω , endowed with non-penetrating boundary conditions. For 4 3 ≤ p ≤ 2 , and initial and forcing data with L p ( Ω ) vorticity we show the existence of a weak solution, enriching and extending the results of Taylor (2000) [32] . In the physical case of a rectangular domain Ω = [ 0 , L 1 ] × [ 0 , L 2 ] , a similar result holds… 
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