»ã±¨±êÌâ (Title)£ºStability of peaked solitary waves for a class of cubic quasilinear shallow-water equations (Ò»ÀàÈý´ÎÄâÏßÐÔdzˮ·½³ÌµÄ¼â·å¹ÂÁ¢²¨µÄ²»±äÐÔ)

»ã±¨ÈË (Speaker)£º µÒ»ªì³ ½ÌÊÚ£¨¹ãÖÝ´óѧ£©

»ã±¨¹¦·ò (Time)£º2025Äê3ÔÂ20ÈÕ(ÖÜËÄ) 13:00

»ã±¨µØÖ· (Place)£ºÌÚѶ»áÒ飺222-381-614

Ô¼ÇëÈË(Inviter)£ºÖìÅå³É

Ö÷°ì²¿ÃÅ£ºÀíѧԺÊýѧϵ

»ã±¨ÌáÒª£ºThis talk is concerned with two classes of cubic quasilinear equations, which can be derived as asymptotic models from shallow-water approximation to the 2D incom pressible Euler equations. One class of the models has homogeneous cubic nonlinearity and includes the integrable modified Camassa¨CHolm (mCH) equation and Novikov equation, and the other class encompasses both quadratic and cubic nonlinearities. It is demonstrated here that both these models possess localized peaked solutions. By constructing a Lyapunov function, these peaked waves are shown to be dynamically stable under small perturbations in the natural energy space H1, without restriction on the sign of the momentum density. In particular, for the homogeneous cubic nonlinear model, we are able to further incorporate a higher-order conservation law to conclude orbital stability in H1 ¡É W1,4. Our analysis is based on a strong use of the conservation laws, the introduction of certain auxiliary functions, and a refined continuity argument.