Stability of steady-states for 3-D hydrodynamic model of unipolar semiconductor with Ohmic contact boundary in hollow ball
In this talk, we consider 3-D radial solutions to the system in a hollow ball, and prove that the 3-D radial subsonic stationary solutions uniquely exist and are asymptotically stable, when the initial perturbations around the subsonic steady-states are small enough. Different from the existing studies on the radial solutions for fluid dynamics where the inner boundary of the hollow ball must be far away from the singular origin, here we may allow the chosen inner boundary arbitrarily close to the singular origin. We also prove the existence of non-flat stationary subsonic solution, which essentially improve and develop the previous studies in this subject. The proof is based on the technical energy estimates in certain weighted Sobolev spaces, where the weight functions are artfully selected to be the distance of the targeted spacial location and the singular point.
This is a joint work with Xiaochun Wu and Yongqian Zhang.