Uniform Local Solvability for the Navier-Stokes Equations with the Coriolis Force
Uniform Local Solvability for the Navier-Stokes Equations with the Coriolis Force
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DOI：
10.4310/maa.2005.v12.n4.a2
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发表时间：
2005-12
影响因子：
0.3
通讯作者：
Y. Giga;K. Inui;A. Mahalov;Shin’ya Matsui
中科院分区：
文献类型：
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作者：
Y. Giga;K. Inui;A. Mahalov;Shin’ya Matsui
建立了具有科里奥利力的不可压缩纳维-斯托克斯方程的柯西问题的唯一局部存在性。限制于散度自由向量场的科里奥利算子是一个零阶伪微分算子，其斜对称矩阵符号与 Riesz 算子相关。它导致纳维-斯托克斯方程中的附加项，其实参数与旋转速度成正比。对于作为所有有限氡测量空间的傅立叶原像的初始数据，在原点处没有点质量，我们证明了旋转速度中存在时间的统一估计。
The unique local existence is established for the Cauchy problem of the incompressible Navier-Stokes equations with the Coriolis force. The Coriolis operator restricted to divergence free vector fields is a zero order pseudodifferential operator with the skew-symmetric matrix symbol related to the Riesz operator. It leads to the additional term in the Navier-Stokes equations which has real parameter being proportional to the speed of rotation. For initial data as Fourier preimage of the space of all finite Radon measures with no point mass at the origin we prove uniform estimate for the existence time in the speed of rotation.