【摘 要】
：
Landau discovered explicit (-1)-homogeneous solutions of 3-d stationary incompressible Navier-Stokes equations with precisely one singularity at the origin.
【机 构】
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RutgersUniversity,USA
【出 处】
：
2016年非线性偏微分方程和变分方法及其应用研讨会(Workshop on Nonlinear PDEs and Cal
论文部分内容阅读
Landau discovered explicit (-1)-homogeneous solutions of 3-d stationary incompressible Navier-Stokes equations with precisely one singularity at the origin. These solutions are axisymmetric with no swirl. Sverak proved in 2006 that these are the only (-1)- homogeneous solutions with one singularity, while Gang Tian and Zhouping Xin proved in 1998 the result under an additional axisymmetry assumption on solutions. Sverak also proved that there are no such solutions in dimension bigger than 3. We construct various (-1)-homogeneous solutions of stationary incompressible Navier- Stokes equations with finite singular rays. For instance, we obtain a three parameter family of (-1)-homogeneous, axisymmetric solutions with nonzero swirl of 3-d stationary incompressible Navier-Stokes equations which are singular only on a single ray. We will also present asymptotic behavior of general (-1)-homogeneous axisymmetric solutions near an isolated singular ray. This is a joint work with Li Li and Xukai Yan.
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