The problem of a self-gravitating scalar field

Speaker:Chuxiao Liu

Time:2021-3-17, 15:00-16:00 pm

Address:数信学院104

Abstract:We study the global initial value problem for Einstein’s equation in the spherically symmetric case with a massless scalar field, we reduce this problem to a nonlinear evolution equation. We prove that the local existence and uniqueness of the solution holds and when the given initial value is sufficiently small, there exists a global solution with good decay property and the final Bondi mass vanishes as u tends to infinity. And when we remove the small assumption of the initial data, there exists a generalized solution of the corresponding equation.