论文标题
三维轴对称不可压缩的Euler方程的伪谱研究的见解
Insights from a pseudospectral study of a potentially singular solution of the three-dimensional axisymmetric incompressible Euler equation
论文作者
论文摘要
我们开发了一个傅立叶 - chebyshev伪直接数值模拟（DNS），以检查径向界限的三维（3D），轴对称欧拉尔方程的潜在奇异溶液[G. lu and T.Y. Hou，Proc。纳特。学院。科学。美国，111.36（2014）]。我们证明：（a）在任何光谱截断的DNS中，通过形成称为Tygers的振荡结构的奇异性时间首先在一维（1d）汉堡和二维（2d）Euler方程中首次研究； （b）可以将分析性方法推广以获得（潜在的）奇点时间的估计值。
We develop a Fourier-Chebyshev pseudospectral direct numerical simulation (DNS) to examine a potentially singular solution of the radially bounded, three-dimensional (3D), axisymmetric Euler equations [G. Luo and T.Y. Hou, Proc. Natl. Acad. Sci. USA, 111.36 (2014)]. We demonstrate that: (a) the time of singularity is preceded, in any spectrally truncated DNS, by the formation of oscillatory structures called tygers, first investigated in the one-dimensional (1D) Burgers and two-dimensional (2D) Euler equations; (b) the analyticity-strip method can be generalized to obtain an estimate for the (potential) singularity time.
