Time: 8th April (Thursday) 13:00 – 14:00
Speaker: Dr. Jinwook Jung (Seoul National Univertisy)
Place: #702, Natural Science Building, Hanyang University
Title : On the pressureless damped Euler-Riesz equations
In this talk, we analyze the pressureless damped Euler–Riesz equations posed in either the whole space or periodic domain. We construct the global-in-time existence and uniqueness of classical solutions for the system around a constant background state. We also establish large-time behaviors of classical solutions showing the solutions towards the equilibrium as time goes to infinity. In the whole space case, we first show the algebraic decay rate of solutions under additional assumptions on the initial data compared to the existence theory. We then refine the argument to have the exponential decay rate of convergence even in the whole space. In the case of the periodic domain, without any further regularity assumptions on the initial data, we provide the exponential convergence of solutions.