| Self-similar Solutions of the Navier–Stokes Equations on Weak Weighted Lorentz Spaces |
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| 基金项目： | Supported by National Natural Science Foundation of China (Grant Nos. 11271330, 11226069 and 11401530), Postdoctoral Science Foundation of China (Grant No. 2013M531446), Natural Science Foundation of Zhejiang Province of China (Grant No. LQ13A010018), and Postdoctoral Science Foundation of Zhejiang Province of China (Grant No. Bsh1202060) |
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| 摘 要： | In the present paper, we prove the existence of global solutions for the Navier–Stokes equations in Rnwhen the initial velocity belongs to the weighted weak Lorentz space Λn,∞(u) with a sufficiently small norm under certain restriction on the weight u. At the same time, self-similar solutions are induced if the initial velocity is, besides, a homogeneous function of degree-1. Also the uniqueness is discussed.
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Self-similar solutions of the Navier-Stokes equations on weak weighted Lorentz spaces |
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| Authors: | Hong Liang Li Jie Cheng Chen |
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| Institution: | 1. Department of Mathematics, Zhejiang International Studies University, Hangzhou 310012, P. R. China;
2. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, P. R. China |
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| Abstract: | In the present paper, we prove the existence of global solutions for the Navier-Stokes equations in Rn when the initial velocity belongs to the weighted weak Lorentz space Λn,∞(u) with a sufficiently small norm under certain restriction on the weight u. At the same time, self-similar solutions are induced if the initial velocity is, besides, a homogeneous function of degree -1. Also the uniqueness is discussed. |
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| Keywords: | Navier-Stokes equations self-similar solutions convolution weighted Lorentz spaces |
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