Speaker: 江宁教授，武汉大学

Inviter: 范晨捷

Title: Incompressible Euler limit from the Boltzmann equation with Maxwell reflection boundary condition in the half-space

Language: Chinese

Time & Venue: 2025.12.09 20:00-21:00 腾讯会议：915-872-951 密码： 89757

Abstract: In this paper, we rigorously justify the incompressible Euler limit of the Boltzmann equation with general Maxwell reflection boundary condition in the half-space. The accommodation coefficient α∈ (0,1] is assumed to be O(1). Our construction of solutions includes the interior fluid part and Knudsen-Prandtl coupled boundary layers. The corresponding solutions to the nonlinear Euler and nonlinear Prandtl systems are taken to be shear flows. Due to the presence of the nonlinear Prandtl layer, the remainder equation loses one order normal derivative. The key technical novelty lies in employing the full conservation laws to convert this loss of the normal derivative into the loss of tangential spatial derivative, avoiding any loss of regularity in time. By working within an analytic L²– L∞ framework, we establish the uniform estimate on the remainder equations, thus justify the validity of the incompressible Euler limit from the Boltzmann equation for the shear flow case.