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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stability of degree-2 Rossby-Haurwitz waves
2度 罗斯比-豪维茨波 稳定性
2023/5/12
Rossby-Haurwitz waves are an important class of explicit solutions to the incompressible Euler equation on a rotating 2-sphere. We will introduce our recent work on the nonlinear stability of degree-2...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the stability of multi-dimensional rarefaction waves
多维 稀薄波 稳定性
2023/4/17
In his pioneering work in 1860, Riemann proposed the Riemann problem and solved it for isentropic gas in terms of shocks and rarefaction waves. It eventually became the foundation of the theory of one...
We show that if p is an odd prime then p−1 X k=0 EkEp−1−k 1 (mod p) and p−3 X k=0 EkEp−3−k (−1)(p−1)/22Ep−3 (mod p),where E0,E1,E2, . . . are ...
Orbital stability of coupled standing waves for systems of non-linear Klein-Gordon equations
standing waves elliptic systems unbounded
2010/12/3
In this work we consider a system of two non-linear waves equa-tions where the non-negative, non-linear term is subcritic and contains a cou-pling term. We show the existence of standing waves solutio...
Well-Posedness and Stability of the Periodic Nonlinear Waves Interactions for the Nenney System
Benney system Well-Posedness Stability of periodic traveling waves
2010/11/30
We establish local well-posedness results in weak periodic function spaces for the Cauchy problem of the Benney system. The Sobolev space H1/2 ×L2 is the lowest regularity attained and also we cover t...
Asymptotic linear stability of solitary water waves
Asymptotic linear stability solitary water waves
2010/11/29
We prove an asymptotic stability result for the water wave equations linearized around
small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounde...
Stability of solitary waves of a generalized two-component Camassa-Holm system
Stability of solitary waves generalized two-component Camassa-Holm system
2010/12/6
We study here the existence of solitary wave solutions of a generalized twocomponent Camassa-Holm system. In addition to those smooth solitary-wave solutions,we show that there are solitary waves with...