5 papers · 1 filter
Exact Blowup Analysis for the Weak-Advection Hou--Li Model
Thomas Y. Hou, Xiang Qin, Xiuyuan Wang
We study self-similar singularity formation for the one-dimensional weak-advection Hou--Li model, a reduced model motivated by the axisymmetric Euler equations. In the periodic set…
Self-similar blow-up profile for the one-dimensional reduction of generalized SQG with infinite energy
Thomas Y. Hou, Xiang Qin, Yannick Sire +1
We study the singularity formation mechanisms of the inviscid generalized Surface Quasi-Geostrophic (gSQG) equation on the whole space and on the upper half-plane $\…
Exact self-similar finite-time blowup of the Hou-Luo model with smooth profiles
De Huang, Xiang Qin, Xiuyuan Wang +1
We show that the 1D Hou-Luo model on the real line admits exact self-similar finite-time blowup solutions with smooth self-similar profiles. The existence of these profiles is esta…
Multi-scale self-similar finite-time blowups of the Constantin-Lax-Majda model for the 3D Euler equations
De Huang, Xiang Qin, Xiuyuan Wang
We construct a new class of asymptotically self-similar finite-time blowups that have two collapsing spatial scales for the 1D Constantin-Lax-Majda model. The larger spatial scale…
Self-similar finite-time blowups with smooth profiles of the generalized Constantin-Lax-Majda model
De Huang, Xiang Qin, Xiuyuan Wang +1
We show that the -parameterized family of the generalized Constantin-Lax-Majda model, also known as the Okamoto-Sakajo-Wunsch model, admits exact self-similar finite-time blowup…