Incompressible limit of all-time solutions to 3-D full Navier–Stokes equations for perfect gas with well-prepared initial condition

  • Dandan Ren
  • Yaobin OuEmail author


In this paper, we prove the incompressible limit of all-time strong solutions to the three-dimensional full compressible Navier–Stokes equations. Here the velocity field and temperature satisfy the Dirichlet boundary condition and convective boundary condition, respectively. The uniform estimates in both the Mach number \({\epsilon\in(0,\overline{\epsilon}]}\) and time \({t\in[0,\infty)}\) are established by deriving a differential inequality with decay property, where \({\overline{\epsilon} \in(0,1]}\) is a constant. Based on these uniform estimates, the global solution of full compressible Navier–Stokes equations with “well-prepared” initial conditions converges to the one of isentropic incompressible Navier–Stokes equations as the Mach number goes to zero.


Incompressible limit Full Navier–Stokes equations All-time solution Dirichlet boundary condition 

Mathematics Subject Classification

35Q35 76N99  76M45 


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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Graduate SchoolChina Academy of Engineering PhysicsBeijingChina
  2. 2.School of InformationRenmin University of ChinaBeijingChina

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