Local well-posedness for the homogeneous Euler equations |
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Authors: | Xin ZhongXing-Ping Wu Chun-Lei Tang |
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Institution: | School of Mathematics and Statistics, Southwest University, Chongqing 400715, People’s Republic of China |
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Abstract: | We introduce Triebel-Lizorkin-Lorentz function spaces, based on the Lorentz Lp,q-spaces instead of the standard Lp-spaces, and prove a local-in-time unique existence and a blow-up criterion of solutions in those spaces for the Euler equations of inviscid incompressible fluid in Rn,n≥2. As a corollary we obtain global existence of solutions to the 2D Euler equations in the Triebel-Lizorkin-Lorentz space. For the proof, we establish the Beale-Kato-Majda type logarithmic inequality and commutator estimates in our spaces. The key methods of proof used are the Littlewood-Paley decomposition and the paradifferential calculus by J.M. Bony. |
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Keywords: | 35Q35 76B03 35B30 |
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