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Applied Analysis
Seminar information archive ～04/02｜Next seminar｜Future seminars 04/03～
| Date, time & place | Thursday 16:00 - 17:30 002Room #002 (Graduate School of Math. Sci. Bldg.) |
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2023/05/18
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Junha Kim (Korea Institute for Advanced Study)
On the wellposedness of generalized SQG equation in a half-plane (English)
https://forms.gle/Cezz3sicY7izDPfq8
Junha Kim (Korea Institute for Advanced Study)
On the wellposedness of generalized SQG equation in a half-plane (English)
[ Abstract ]
In this talk, we investigate classical solutions to the α-SQG in a half-plane, which reduces to the 2D Euler equations and SQG equation for α=0 and α=1, respectively. When α∈(0,1/2], we establish that α-SQG is well-posed in appropriate anisotropic Lipschitz spaces. Moreover, we prove that every solution with smooth initial data that is compactly supported and not vanishing on the boundary has infinite Cβ-norm instantaneously where β>1−α. In the case of α∈(1/2,1], we show the nonexistence of solutions in Cα. This is a joint work with In-Jee Jeong and Yao Yao.
[ Reference URL ]In this talk, we investigate classical solutions to the α-SQG in a half-plane, which reduces to the 2D Euler equations and SQG equation for α=0 and α=1, respectively. When α∈(0,1/2], we establish that α-SQG is well-posed in appropriate anisotropic Lipschitz spaces. Moreover, we prove that every solution with smooth initial data that is compactly supported and not vanishing on the boundary has infinite Cβ-norm instantaneously where β>1−α. In the case of α∈(1/2,1], we show the nonexistence of solutions in Cα. This is a joint work with In-Jee Jeong and Yao Yao.
https://forms.gle/Cezz3sicY7izDPfq8
