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The domain of analyticity of solutions to the three-dimensional Euler equations in a half space

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  • We address the problem of analyticity up to the boundary of solutions to the Euler equations in the half space. We characterize the rate of decay of the real-analyticity radius of the solution $u(t)$ in terms of exp$\int_{0}^{t} $||$ \nabla u(s) $|| L ds , improving the previously known results. We also prove the persistence of the sub-analytic Gevrey-class regularity for the Euler equations in a half space, and obtain an explicit rate of decay of the radius of Gevrey-class regularity.
    Mathematics Subject Classification: Primary: 76B03; Secondary: 35L60.

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