Local well-posedness of solutions to the boundary layer equations for 2D compressible flow

2021 ◽  
Vol 493 (2) ◽  
pp. 124565
Author(s):  
Long Fan ◽  
Lizhi Ruan ◽  
Anita Yang
Keyword(s):  
Boundary Layer ◽  
Compressible Flow ◽  
Well Posedness ◽  
Boundary Layer Equations

Transformations of the boundary-layer equations for rotating flows

1968 ◽  
Vol 33 (1) ◽  
pp. 113-126
Author(s):  
N. Rott ◽  
J. T. Ohrenberger
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Compressible Flow ◽  
Incompressible Flow ◽  
Flow Problem ◽  
Rotating Flows ◽  
Governing Equations ◽  
Boundary Layer Equations ◽  
Axis Of Symmetry ◽  
Semi Empirical

The boundary layer on an axisymmetric surface above which the flow is rotating about the axis of symmetry is considered. Transformations of the governing equations which permit the generalizations of a known solution for one meridian shape in incompressible flow to a family of meridian shapes are shown to exist. For compressible flow, a transformation of the Stewartson-Illingworth type was found which reduces a compressible flow problem to an incompressible case. Also, remarks are made concerning the invariance of the turbulent boundary-layer integral equations assuming particular semi-empirical shear laws.

A boundary layer theorem, with applications to rotating cylinders

1957 ◽  
Vol 2 (1) ◽  
pp. 89-99 ◽  
Author(s):  
M. B. Glauert
Keyword(s):  
Boundary Layer ◽  
Circular Cylinder ◽  
Compressible Flow ◽  
Slip Flow ◽  
Three Dimensional ◽  
Time Dependent ◽  
Boundary Layer Equations ◽  
Rotating Circular Cylinder ◽  
Quantitative Results ◽  
Explicit Formulae

If, in a given solution of the boundary layer equations, the position of the wall is varied, then additional solutions of the boundary layer equations may be deduced. The theorem considers the nature of such solution, for the general case of time-dependent three-dimensional compressible flow.Applications of the theorem arise in several different fields, and it is shown that useful quantitative results can often be obtained with the minimum of calculation. In this paper, chief attention is focused on the case of a rotating circular cylinder, and explicit formulae are developed for the skin friction, valid for sufficiently low rotational speeds. The important results which the theorem gives for slip flow have been noted by previous extenions to these previous treatments are made. Other applications of the theorem are briefly mentioned.

scholarly journals Well-posedness in Sobolev spaces of the two-dimensional MHD boundary layer equations without viscosity

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Wei-Xi Li ◽  
Rui Xu
Keyword(s):  
Boundary Layer ◽  
Sobolev Spaces ◽  
Tangential Component ◽  
Well Posedness ◽  
Two Dimensional ◽  
Uniqueness Of Solutions ◽  
Layer System ◽  
Boundary Layer Equations ◽  
Mhd Boundary Layer ◽  
Liu Xie

<p style='text-indent:20px;'>We consider the two-dimensional MHD Boundary layer system without hydrodynamic viscosity, and establish the existence and uniqueness of solutions in Sobolev spaces under the assumption that the tangential component of magnetic fields dominates. This gives a complement to the previous works of Liu-Xie-Yang [Comm. Pure Appl. Math. 72 (2019)] and Liu-Wang-Xie-Yang [J. Funct. Anal. 279 (2020)], where the well-posedness theory was established for the MHD boundary layer systems with both viscosity and resistivity and with viscosity only, respectively. We use the pseudo-differential calculation, to overcome a new difficulty arising from the treatment of boundary integrals due to the absence of the diffusion property for the velocity.</p>

Integration of the boundary-layer equations for a plane in compressible flow with heat transfer

1955 ◽  
Vol 231 (1185) ◽  
pp. 274-280 ◽  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Prandtl Number ◽  
Pressure Gradient ◽  
Drag Coefficient ◽  
Compressible Flow ◽  
Equations Of Motion ◽  
Main Flow ◽  
Physical Constants ◽  
Boundary Layer Equations

The equations of motion of compressible viscous flow with vanishing pressure gradient past a plane are integrated in semi-convergent expressions, for the case when the physical constants depend on temperature and the Prandtl number σ is close to unity. Simple expressions are obtained for the temperature and velocity distributions in the boundary layer, the drag coefficient, and their dependence on the physical constants; they contain the well-known results and several new ones. For the case when the temperature of the boundary is either above, or not much below, the temperature of the main flow, the results obtained closely agree with Crocco’s numerical computations.

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