LINEAR STABILITY OF THE COUETTE FLOW IN THE 3D ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS

作者：Zeng, Lan^*; Zhang, Zhifei; Zi, Ruizhao

来源：SIAM Journal on Mathematical Analysis, 2022, 54(5): 5698-5741.

DOI：10.1137/21M1438499

• compressible Navier-Stokes equations
• Couette flow
• enhanced dissipation

Consider the linear stability of the three dimensional (3D) isentropic compressible Navier-Stokes equations on T x R x T. We prove the enhanced dissipation phenomenon for the linearized isentropic compressible Navier-Stokes equations around the Couette flow (y, 0, 0)(inverted perpendicular). Moreover, the lift-up phenomenon is also shown in this paper. In particular, due to the loss of the incompressibility condition, the upper bounds for the x-average of the perturbed streamwise velocity u10 in this paper are worse than those in the corresponding 3D incompressible Navier-Stokes equations [J. Bedrossian, P. Germain, and N. Masmoudi, Ann. Math., 185 (2017), pp. 541-608].

• 单位
  北京大学