123 research outputs found

    Global well-posedness for the 2 D quasi-geostrophic equation in a critical Besov space

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    We show that the the 2 D quasi-geostrophic equation has global and unique strong solution, when the (large) data belongs in the critical, scale invariant space \dot{B}^{2-2\al}_{2, \infty}\cap L^{2/(2\al-1)}

    Optimal solvability for the Dirichlet and Neumann problem in dimension two

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    We show existence and uniqueness for the solutions of the regularity and the Neumann problems for harmonic functions on Lipschitz domains with data in the Hardy spaces H^p, p>2/3, where This in turn implies that solutions to the Dirichlet problem with data in the Holder class C^{1/2}(\partial D) are themselves in C^{1/2}(D). Both of these results are sharp. In fact, we prove a more general statement regarding the H^p solvability for divergence form elliptic equations with bounded measurable coefficients. We also prove similar solvability result for the regularity and Dirichlet problem for the biharmonic equation on Lipschitz domains
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