Prandtl boundary layer expansions of steady Navier-Stokes flows over a moving plate

Preprint English OPEN
Guo, Yan ; Nguyen, Toan T. (2014)
  • Subject: Mathematical Physics | Mathematics - Analysis of PDEs
    arxiv: Mathematics::Analysis of PDEs | Physics::Fluid Dynamics

This paper concerns the validity of the Prandtl boundary layer theory in the inviscid limit for steady incompressible Navier-Stokes flows. The stationary flows, with small viscosity, are considered on $[0,L]\times \mathbb{R}_{+}$, assuming a no-slip boundary condition over a moving plate at $y=0$. We establish the validity of the Prandtl boundary layer expansion and its error estimates.
  • References (4)

    [12] Oleinik, O. A. ; Samokhin, V. N. Mathematical models in boundary layer theory. Applied Mathematics and Mathematical Computation, 15. Chapman & Hall/CRC, Boca Raton, FL, 1999. x+516 pp.

    [13] M. Orlt, Regularity for Navier-Stokes in domains with corners, PhD Thesis, 1998 (in German).

    [14] M. Orlt and A.-M. Sa¨ndig, Regularity of viscous Navier-Stokes flows in nonsmooth domains. Boundary value problems and integral equations in nonsmooth domains (Luminy, 1993), 185- 201, Lecture Notes in Pure and Appl. Math., 167, Dekker, New York, 1995.

    [15] M. Sammartino and R. Caflisch, Zero viscosity limit for analytic solutions of the Navier-Stokes equation on a half-space. I. Existence for Euler and Prandtl equations. Comm. Math. Phys. 192 (1998), no. 2, 433-461.

  • Metrics
    No metrics available
Share - Bookmark