Existence and Singularities for the Prandtl Boundary Layer Equations

Prandtl's boundary layer equations, first formulated in 1904, resolve the differences between the viscous and inviscid description of fluid flows. This paper presents a review of mathematical results, both analytic and computational, on the unsteady boundary layer equations. This includes a review of the derivation and basic properties of the equations, singularity formation, well-posedness results, and infinite Reynolds number limits.

[1]  Tosio Kato,et al.  Quasi-linear equations of evolution, with applications to partial differential equations , 1975 .

[2]  Tosio Kato Nonstationary flows of viscous and ideal fluids in R3 , 1972 .

[3]  Russel E. Caflisch,et al.  Zero Viscosity Limit for Analytic Solutions of the Navier-Stokes Equation on a Half-Space.¶ II. Construction of the Navier-Stokes Solution , 1998 .

[4]  S. F. Shen,et al.  The spontaneous generation of the singularity in a separating laminar boundary layer , 1980 .

[5]  S. Goldstein,et al.  ON LAMINAR BOUNDARY-LAYER FLOW NEAR A POSITION OF SEPARATION , 1948 .

[6]  H. Swann The convergence with vanishing viscosity of nonstationary Navier-Stokes flow to ideal flow in ₃ , 1971 .

[7]  E Weinan,et al.  BLOWUP OF SOLUTIONS OF THE UNSTEADY PRANDTL'S EQUATION , 1997 .

[8]  Tosio Kato,et al.  Remarks on Zero Viscosity Limit for Nonstationary Navier- Stokes Flows with Boundary , 1984 .

[9]  V. N. Samokhin,et al.  Mathematical Models in Boundary Layer Theory , 1999 .

[10]  R. Temam,et al.  The convergence of the solutions of the Navier-Stokes equations to that of the Euler equations , 1997 .

[11]  Russel E. Caflisch,et al.  Zero Viscosity Limit for Analytic Solutions, of the Navier-Stokes Equation on a Half-Space.¶I. Existence for Euler and Prandtl Equations , 1998 .

[12]  Nader Masmoudi,et al.  The Euler Limit of the Navier‐Stokes Equations, and Rotating Fluids with Boundary , 1998 .

[13]  S. Cowley Computer extension and analytic continuation of Blasius’ expansion for impulsive flow past a circular cylinder , 1983, Journal of Fluid Mechanics.

[14]  M. Safonov,et al.  The abstract cauchy‐kovalevskaya theorem in a weighted banach space , 1995 .