Exact periodic solutions of the generalized Constantin-Lax-Majda
equation with dissipation
Exact periodic solutions of the generalized Constantin-Lax-Majda
equation with dissipation
We present exact pole dynamics solutions to the generalized Constantin-Lax-Majda (gCLM) equation in a periodic geometry with dissipation $-\Lambda^\sigma$, where its spatial Fourier transform is $\widehat{\Lambda^\sigma}=|k|^\sigma$. The gCLM equation is a simplified model for singularity formation in the 3D incompressible Euler equations. It includes an advection term with parameter $a$, …