In this paper, a sequence of solutions to the one-dimensional motion of a radiating gas are con- structed. Furthermore, when the absorption coefficient a tends to oo, the above solutions converge to the rarefaction wa...In this paper, a sequence of solutions to the one-dimensional motion of a radiating gas are con- structed. Furthermore, when the absorption coefficient a tends to oo, the above solutions converge to the rarefaction wave, which is an elementary wave pattern of gas dynamics, with a convergence rate α -1/3|lnα|2.展开更多
In the paper,we establish the existence of steady boundary layer solution of Boltzmann equation with specular boundary condition in Lx,v2∩Lx,v∞in half-space.The uniqueness,continuity and exponential decay of the sol...In the paper,we establish the existence of steady boundary layer solution of Boltzmann equation with specular boundary condition in Lx,v2∩Lx,v∞in half-space.The uniqueness,continuity and exponential decay of the solution are obtained,and such estimates are important to prove the Hilbert expansion of Boltzmann equation for half-space problem with specular boundary condition.展开更多
The history of hyperbolic system of conservation laws can date back to the eighteenth century,after several works of the natural philosophers,most notably L.Euler.The compressible Euler system,consisting of mass,momen...The history of hyperbolic system of conservation laws can date back to the eighteenth century,after several works of the natural philosophers,most notably L.Euler.The compressible Euler system,consisting of mass,momentum and energy in the divergence form,is the prototypical model of the hyperbolic system of conservation laws,and its main feature is the shock formation in a finite time no matter how the initial values smooth.This poses huge challenges in the mathematical analysis.展开更多
基金Supported in part by NSFC Grant No.10825102 for Outstanding Young scholarsNational Basic Research Program of China(973 Program),No.2011CB808002Youth foundation of Chinese NSF 11301344
文摘In this paper, a sequence of solutions to the one-dimensional motion of a radiating gas are con- structed. Furthermore, when the absorption coefficient a tends to oo, the above solutions converge to the rarefaction wave, which is an elementary wave pattern of gas dynamics, with a convergence rate α -1/3|lnα|2.
基金supported by National Key R&D Program of China No.2021YFA1000800by the National Natural Science Foundation of China(Nos.12288201,12022114,12071439)。
文摘In the paper,we establish the existence of steady boundary layer solution of Boltzmann equation with specular boundary condition in Lx,v2∩Lx,v∞in half-space.The uniqueness,continuity and exponential decay of the solution are obtained,and such estimates are important to prove the Hilbert expansion of Boltzmann equation for half-space problem with specular boundary condition.
文摘The history of hyperbolic system of conservation laws can date back to the eighteenth century,after several works of the natural philosophers,most notably L.Euler.The compressible Euler system,consisting of mass,momentum and energy in the divergence form,is the prototypical model of the hyperbolic system of conservation laws,and its main feature is the shock formation in a finite time no matter how the initial values smooth.This poses huge challenges in the mathematical analysis.