A Remark on L∞ Solutions to the 2-D Navier–Stokes Equations |
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| Authors: | Okihiro Sawada Yasushi Taniuchi |
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| Affiliation: | (1) Department of Mathematical Science, Waseda University, Shinjuku 169-8555, Japan;(2) Department of Mathematical Sciences, Shinshu University, Matsumoto 390-8621, Japan |
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| Abstract: | A single-exponential growth estimate of the solutions to the 2-dimensional Navier–Stokes equations in the whole space for nondecaying initial velocity is established. The crucial idea is to decompose velocity into high and low frequency parts. Moreover, if the linear term and the vorticity decay exponentially, the velocity is bounded uniformly in time. |
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| Keywords: | 35Q30 35Q35 |
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