报告题目： Asymptotic analysis on the modelling of the shallow-water waves with the Coriolis effect
报 告 人：刘 越 教授（美国德克萨斯大学阿灵顿分校）
In this talk, a mathematical model of long-crested water waves propagating mainly in one direction with the effect of Earth''s rotation is derived by following the formal asymptotic procedures. Such a model equation is analogous to the Camassa-Holm approximation of the two-dimensional incompressible and irrotational Euler equations and has a formal bi-Hamiltonian structure. Its solution corresponding to physically relevant initial perturbations is more accurate on a much longer time scale. It is shown that the deviation of the free surface can be determined by the horizontal velocity at a certain depth in the second-order approximation. The effects of the Coriolis force caused by the Earth rotation and nonlocal higher nonlinearities on blow-up criteria and wave-breaking phenomena are also investigated. Our refined analysis is approached by applying the method of characteristics and conserved quantities to the Riccati-type differential inequality.
刘越教授主要研究领域: 数学物理与偏微分方程。在水波方程孤立子轨道稳定性、尖峰孤立理论、非线性色散波方程的整体存在性等研究上取得一些列进展，其研究成果已在《Comm. Pure Appl. Math.》、《Comm. Math. Phys.》、《Advance in Math.》、《Arch. Rational Mech. Anal.》、《J. Funct. Anal.》、《Transaction of AMS》、《Communications in PDE》、《J. Differential Equations》等上发表80余篇研究论文，研究成果多次被国内外学者引用。