수학과

6월 18일 (수) 에 열리는 수학과 김준하 교수 초청 세미나를 안내 드립니다.

학우들의 많은 관심과 참여를 부탁 드립니다.

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 1. 연사: 방제형 박사 (Westlake University in Hangzhou)

 2. 일시: 2025년 6월 18일(수) 15:30~16:30

 3. 장소: 팔달관 621호

 4. Title: Rigidity of Steady Solutions to the Navier-Stokes Equations in High Dimensions

 5. Abstract:

Solutions with scaling-invariant bounds, such as self-similar solutions, play an important role in understanding the regularity and asymptotic structures of solutions to the Navier-Stokes equations. On the other hand, the higher dimensional steady Navier-Stokes equations have attracted attention because the 5D steady case shares the same scaling dimension as the 3D evolutionary case. We proved that any steady solution $u$ must be trivial if $|u(x)|\leq C/|x|$ (scaling-invariant bound) in the entire Euclidean space for some constant $C>0$ when the dimension is at least 4, without assuming any smallness, self-similarity or axisymmetry. Our main idea is to use weighted energy estimates and prove a sign property of the total head pressure. As applications, we also proved a removable singularity in a punctured domain and identified a leading term describing the large-distance behavior of a general solution in an exterior domain. This is a collaboration with Changfeng Gui (Univ. of Macau), Chunjing Xie, Hao Liu (Shanghai Jiaotong Univ.) and Yun Wang (Soochow Univ.)

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