Xiaoyu Luo

activity

20222024

C^{2}

vortex patches

6 citations · 8 across the 3 of their papers we have counts for

collaborators

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3 papers · 1 filter

math.AP2024

Eulerian uniqueness of the $α$ -SQG patch problem

Xiaoyutao Luo

We consider the patch problem of the $α$ -SQG equation with $α = 0$ being the 2D Euler and $α = \frac{1}{2}$ the SQG equations respectively. In the Eulerian setting, we prove the uniqu…

math.AP2023★ 2 cited

The $α$ -SQG patch problem is illposed in $C^{2, β}$ and $W^{2, p}$

Alexander Kiselev, Xiaoyutao Luo

We consider the patch problem for the $α$ -SQG system with the values $α = 0$ and $α = \frac{1}{2}$ being the 2D Euler and the SQG equations respectively. It is well-known that the Eul…

math.AP2022★ 6 cited

Illposedness of $C^{2}$ vortex patches

Alexander Kiselev, Xiaoyutao Luo

It is well known that vortex patches are wellposed in $C^{1, α}$ if $0 < α < 1$ . In this paper, we prove the illposedness of $C^{2}$ vortex patches. The setup is to consider the vortex…

Eulerian uniqueness of the α-SQG patch problem

The α-SQG patch problem is illposed in C2,β and W2,p

Illposedness of C2 vortex patches

Eulerian uniqueness of the $α$ -SQG patch problem

The $α$ -SQG patch problem is illposed in $C^{2, β}$ and $W^{2, p}$

Illposedness of $C^{2}$ vortex patches