On the radius of analyticity of solutions to the three-dimensional Euler equations
On the radius of analyticity of solutions to the three-dimensional Euler equations
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DOI：
10.1090/s0002-9939-08-09693-7
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发表时间：
2008-09
期刊：
影响因子：
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通讯作者：
I. Kukavica;V. Vicol
中科院分区：
文献类型：
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作者：
I. Kukavica;V. Vicol
研究不可压缩欧拉方程光滑解u的解析性问题。若初始数据为实解析，则只要f t 0∥∇u（·，s）∥L∞ds <∞，解保持实解析。利用gevrey类方法，我们得到了空间解析性半径的下界，其代数依赖于exp∫t 0∥∇u（·，s）∥L∞ds。特别是，我们以肯定的方式回答了莱弗莫尔和奥利弗提出的一个问题。
We address the problem of analyticity of smooth solutions u of the incompressible Euler equations. If the initial datum is real-analytic, the solution remains real-analytic as long as f t 0 ∥∇u(·, s)∥ L∞ ds < ∞. Using a Gevrey-class approach we obtain lower bounds on the radius of space analyticity which depend algebraically on exp ∫ t 0 ∥∇u(·,s)∥ L∞ ds. In particular, we answer in the positive a question posed by Levermore and Oliver.