The study of the hydrodynamic limit of the Boltzmann equation with physical boundary is a challenging problem due to the appearance of the viscous and Knudsen boundary layers.In this paper,the hydrodynamic limit from ...The study of the hydrodynamic limit of the Boltzmann equation with physical boundary is a challenging problem due to the appearance of the viscous and Knudsen boundary layers.In this paper,the hydrodynamic limit from the Boltzmann equation with the specular reflection boundary condition to the incompressible Euler equations in a channel is investigated.Based on the multi-scaled Hilbert expansion,the equations with boundary conditions and compatibility conditions for interior solutions,and viscous and Knudsen boundary layers are derived under different scaling,respectively.Then,some uniform estimates for the interior solutions,and viscous and Knudsen boundary layers are established.With the help of the L^(2)-L^(∞) framework and the uniform estimates obtained above,the solutions to the Boltzmann equation are constructed by the truncated Hilbert expansion with multiscales,and hence the hydrodynamic limit in the incompressible Euler level is justified.展开更多
基金supported by National Key R&D Program of China(Grant No.2021YFA1000800)National Natural Science Foundation of China(Grant No.12288201)+3 种基金supported by National Natural Science Foundation of China(Grant Nos.12022114 and 12288201)CAS Project for Young Scientists in Basic Research(Grant No.YSBR-031)Youth Innovation Promotion Association of CAS(Grant No.2019002)supported by National Natural Science Foundation of China(Grant No.12201209)。
文摘The study of the hydrodynamic limit of the Boltzmann equation with physical boundary is a challenging problem due to the appearance of the viscous and Knudsen boundary layers.In this paper,the hydrodynamic limit from the Boltzmann equation with the specular reflection boundary condition to the incompressible Euler equations in a channel is investigated.Based on the multi-scaled Hilbert expansion,the equations with boundary conditions and compatibility conditions for interior solutions,and viscous and Knudsen boundary layers are derived under different scaling,respectively.Then,some uniform estimates for the interior solutions,and viscous and Knudsen boundary layers are established.With the help of the L^(2)-L^(∞) framework and the uniform estimates obtained above,the solutions to the Boltzmann equation are constructed by the truncated Hilbert expansion with multiscales,and hence the hydrodynamic limit in the incompressible Euler level is justified.
