数学研究所
调和分析及其应用研究中心
学术报告
偏微分方程研讨班
Speaker: 郝田田（北京大学）
Inviter: 张平 院士
Language: Chinese
Title: Geometric blow-up criteria for non-homogeneous incompressible Euler equations in two dimensions
Time&Venue: 2025年3月9日（星期日）15:00-17:00& 晨兴410
Abstract: I will discuss the geometric blow-up criteria for the two-dimensional non-homogeneous incompressible Euler equations. While the homogeneous Euler equations (with constant density) are globally well-posed, the global well-posedness of solutions for the non-homogeneous case remains an open problem. Recently, F. Fanelli introduced an innovative approach that determines the blow-up or continuation of solutions by controlling the derivatives of the velocity field only along the direction of the density gradient. Compared to traditional blow-up criteria based on the Lipschitz norm, this geometric method is more concise and offers a new perspective on understanding the global behavior of solutions.
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