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arXiv · 1106.3704

Vanishing viscosity limits for the degenerate lake equations with Navier boundary conditions

Quansen Jiu·Dongjuan Niu·Jiahong Wu
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Abstract

The paper is concerned with the vanishing viscosity limit of the two-dimensional degenerate viscous lake equations when the Navier slip conditions are prescribed on the impermeable boundary of a simply connected bounded regular domain. When the initial vorticity is in the Lebesgue space $L^q$ with $2<q\le\infty$, we show the degenerate viscous lake equations possess a unique global solution and the solution converges to a corresponding weak solution of the inviscid lake equations. In the special case when the vorticity is in $L^\infty$, an explicit convergence rate is obtained.

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Quansen Jiu, Dongjuan Niu, Jiahong Wu. 2011-06-19. Vanishing viscosity limits for the degenerate lake equations with Navier boundary conditions. https://doi.org/10.1088/0951-7715%2F25%2F3%2F641

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