Dia: Dimecres, 20 de juliol de 2022
Lloc: Aula T2 (2n pis), Facultat de Matemàtiques i Informàtica, UB.
També ONLINE https://ub-edu.zoom.us/j/99239919625?pwd=V0hUZXQvV29OMCs0aTJnYkFiV1I2UT09
Zoom session Id: 992 3991 9625, pass: 650673
A càrrec de: Jonathan Jaquette, Boston University
Títol: Global dynamics and blowup in some quadratic PDEs
Resum: Conservation laws and Lyapunov functions are powerful tools for proving the global existence of stability of solutions, but for many complex systems these tools are insufficient to completely understand non-perturbative dynamics. In this talk I will discuss a complex-scalar PDE which may be seen as a toy model for vortex streching in fluid flow, and cannot be neatly categorized as conservative nor dissipative.In a recent series of papers we have shown that this equation exhibits rich dynamical behavior that exist globally in time: non-trivial equilibria, homoclinic orbits, heteroclinic orbits, and integrable subsystems foliated by periodic orbits. On the other side of the coin, we show several mechanisms by which solutions can blowup. I will discuss these results, and current work toward understanding unstable blowup and wave turbulence.
Last updated: Mon Jul 18 10:34:53 2022