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Guo, Yan; Nguyen, Toan T. (2014)
Languages: English
Types: Preprint
Subjects: Mathematical Physics, Mathematics - Analysis of PDEs

Classified by OpenAIRE into

arxiv: Physics::Fluid Dynamics, Mathematics::Analysis of PDEs
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.
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    • [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.
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