A type nonlinear differential difference system ·↑x(i)(t)=n↑∑↑j=1[αijfij(xj(t))+bijgij(xj(t-τj))](i=1,2,…,n) is studied.We give some theorems which decide the almost exponential asymptotic stability of the...A type nonlinear differential difference system ·↑x(i)(t)=n↑∑↑j=1[αijfij(xj(t))+bijgij(xj(t-τj))](i=1,2,…,n) is studied.We give some theorems which decide the almost exponential asymptotic stability of the zero so-lution.展开更多
This paper studies the incompressible limit and stability of global strong solutions to the threedimensional full compressible Navier-Stokes equations, where the initial data satisfy the "well-prepared" cond...This paper studies the incompressible limit and stability of global strong solutions to the threedimensional full compressible Navier-Stokes equations, where the initial data satisfy the "well-prepared" conditions and the velocity field and temperature enjoy the slip boundary condition and convective boundary condition, respectively. The uniform estimates with respect to both the Mach number ∈(0, ∈] and time t ∈ [0, ∞) are established by deriving a differential inequality with decay property, where ∈∈(0, 1] is a constant.As the Mach number vanishes, the global solution to full compressible Navier-Stokes equations converges to the one of isentropic incompressible Navier-Stokes equations in t ∈ [0, +∞). Moreover, we prove the exponentially asymptotic stability for the global solutions of both the compressible system and its limiting incompressible system.展开更多
文摘A type nonlinear differential difference system ·↑x(i)(t)=n↑∑↑j=1[αijfij(xj(t))+bijgij(xj(t-τj))](i=1,2,…,n) is studied.We give some theorems which decide the almost exponential asymptotic stability of the zero so-lution.
基金supported by National Natural Science Foundation of China (Grant No. 11471334)Program for New Century Excellent Talents in University (Grant No. NCET-12-0085)
文摘This paper studies the incompressible limit and stability of global strong solutions to the threedimensional full compressible Navier-Stokes equations, where the initial data satisfy the "well-prepared" conditions and the velocity field and temperature enjoy the slip boundary condition and convective boundary condition, respectively. The uniform estimates with respect to both the Mach number ∈(0, ∈] and time t ∈ [0, ∞) are established by deriving a differential inequality with decay property, where ∈∈(0, 1] is a constant.As the Mach number vanishes, the global solution to full compressible Navier-Stokes equations converges to the one of isentropic incompressible Navier-Stokes equations in t ∈ [0, +∞). Moreover, we prove the exponentially asymptotic stability for the global solutions of both the compressible system and its limiting incompressible system.
