TY - JOUR
T1 - STUDY OF BOUNDARY LAYERS IN COMPRESSIBLE NON-ISENTROPIC FLOWS
AU - LIU, Cheng-Jie
AU - WANG, Ya-Guang
AU - YANG, Tong
PY - 2021/12
Y1 - 2021/12
N2 - In this note, we review our recent study on boundary layer problems in compressible non-isentropic flows with non-slip boundary condition for the velocity, in the small viscosity and heat conductivity limit. By multi-scale analysis, we derive the problems of viscous layer profiles and thermal layer profiles for different scales of viscosity and heat conductivity, from which we obtain the interaction mechanism of viscous layers and thermal layers. Then, when the viscosity goes to zero slower than or at the same rate as the heat conductivity, we give a well-posedness result of the twodimensional viscous layer problem, which is the Prandtl type equations coupled with a degenerated parabolic equation, in the class of tangential velocity being strictly monotonic in the normal variable. Last, when the viscosity goes to zero faster than the heat conductivity, we study the stability of the thermal layer problem at a shear flow in two or three space variables, which is an inviscid Prandtl type equations coupled with a degenerated parabolic equation.
AB - In this note, we review our recent study on boundary layer problems in compressible non-isentropic flows with non-slip boundary condition for the velocity, in the small viscosity and heat conductivity limit. By multi-scale analysis, we derive the problems of viscous layer profiles and thermal layer profiles for different scales of viscosity and heat conductivity, from which we obtain the interaction mechanism of viscous layers and thermal layers. Then, when the viscosity goes to zero slower than or at the same rate as the heat conductivity, we give a well-posedness result of the twodimensional viscous layer problem, which is the Prandtl type equations coupled with a degenerated parabolic equation, in the class of tangential velocity being strictly monotonic in the normal variable. Last, when the viscosity goes to zero faster than the heat conductivity, we study the stability of the thermal layer problem at a shear flow in two or three space variables, which is an inviscid Prandtl type equations coupled with a degenerated parabolic equation.
KW - compressible non-isentropic flows
KW - small viscosity and heat conductivity limit
KW - viscous layers and thermal layers
KW - well-posedness
KW - ZERO-VISCOSITY LIMIT
KW - NAVIER-STOKES EQUATIONS
KW - PRANDTL EQUATIONS
KW - ANALYTIC SOLUTIONS
KW - GLOBAL EXISTENCE
KW - INVISCID LIMIT
KW - ILL-POSEDNESS
KW - HALF-SPACE
KW - STABILITY
UR - http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=LinksAMR&SrcApp=PARTNER_APP&DestLinkType=FullRecord&DestApp=WOS&KeyUT=000814098500003
U2 - 10.4310/maa.2021.v28.n4.a3
DO - 10.4310/maa.2021.v28.n4.a3
M3 - 21_Publication in refereed journal
VL - 28
SP - 453
EP - 466
JO - Methods and Applications of Analysis
JF - Methods and Applications of Analysis
SN - 1073-2772
IS - 4
ER -