speaker: Yuejun Peng, Université Clermont Auvergne, Professor

time: 2024.5.29，3:00-4:00 PM   

place: Teaching building 308

Abstract:

In this talk, I consider the Cauchy problem for isentropic Euler equations with relaxation close to the isothermal case. I first show that the problem admits a unique smooth solution when either the relaxation time or the initial datum is sufficiently small. Then, in an appropriate time scaling, I establish error estimates of the convergence of the large density of the Euler equations toward the solution of the porous medium equation as the relaxation time tends to zero. Besides energy estimates, a key step to prove these results is a uniform estimate of a quantity related to Darcy's law.