A note on the -stability of boundary layers in viscous conservation laws

2008 ◽  
Vol 68 (9) ◽  
pp. 2677-2680 ◽  
Author(s):  
R. Cavazzoni
Keyword(s):  
Conservation Laws ◽  
Boundary Layers ◽  
Viscous Conservation Laws ◽  
The Stability

STABILITY OF SHOCK PROFILES FOR NONCONVEX SCALAR VISCOUS CONSERVATION LAWS

1995 ◽  
Vol 05 (03) ◽  
pp. 279-296 ◽  
Author(s):  
MING MEI
Keyword(s):  
Conservation Laws ◽  
Decay Rates ◽  
Asymptotically Stable ◽  
Time Decay ◽  
Shock Condition ◽  
Viscous Conservation Laws ◽  
Time Decay Rates ◽  
Shock Profiles ◽  
Degenerate Shock ◽  
The Stability

This paper is to study the stability of shock profiles for nonconvex scalar viscous conservation laws with the nondegenerate and the degenerate shock conditions by means of an elementary energy method. In both cases, the shock profiles are proved to be asymptotically stable for suitably small initial disturbances. Moreover, in the case of nondegenerate shock condition, time decay rates of asymptotics are also obtained.

Lp ENERGY METHOD FOR MULTI-DIMENSIONAL VISCOUS CONSERVATION LAWS AND APPLICATION TO THE STABILITY OF PLANAR WAVES

2004 ◽  
Vol 01 (03) ◽  
pp. 581-603 ◽  
Author(s):  
SHUICHI KAWASHIMA ◽  
SHINYA NISHIBATA ◽  
MASATAKA NISHIKAWA
Keyword(s):  
Conservation Laws ◽  
Energy Method ◽  
Optimal Convergence Rate ◽  
Estimates Of Solutions ◽  
Interpolation Inequalities ◽  
Optimal Decay ◽  
Viscous Conservation Laws ◽  
The Cauchy Problem ◽  
Whole Space ◽  
The Stability

We introduce a new Lp energy method for multi-dimensional viscous conservation laws. Our energy method is useful enough to derive the optimal decay estimates of solutions in the W1,p space for the Cauchy problem. It is also applicable to the problem for the stability of planar waves in the whole space or in the half space, and gives the optimal convergence rate toward the planar waves as time goes to infinity. This energy method makes use of several special interpolation inequalities.

Modeling of External Pressure Gradient Influence on the Stability of Disturbances in the Boundary Layers of Compressed Gas

2013 ◽  
Vol 8 (4) ◽  
pp. 64-75
Author(s):  
Sergey Gaponov ◽  
Natalya Terekhova
Keyword(s):  
Mach Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Leading Edge ◽  
External Pressure ◽  
Transition To Turbulence ◽  
Compressed Gas ◽  
High Mach ◽  
The Stability ◽  
Very High

This work continues the research on modeling of passive methods of management of flow regimes in the boundary layers of compressed gas. Authors consider the influence of pressure gradient on the evolution of perturbations of different nature. For low Mach number M = 2 increase in pressure contributes to an earlier transition of laminar to turbulent flow, and, on the contrary, drop in the pressure leads to a prolongation of the transition to turbulence. For high Mach number M = 5.35 found that the acoustic disturbances exhibit a very high dependence on the sign and magnitude of the external gradient, with a favorable gradient of the critical Reynolds number becomes smaller than the vortex disturbances, and at worst – boundary layer is destabilized directly on the leading edge

scholarly journals Sparse + low-energy decomposition for viscous conservation laws

2015 ◽  
Vol 288 ◽  
pp. 150-166 ◽  
Author(s):  
Thomas Y. Hou ◽  
Qin Li ◽  
Hayden Schaeffer
Keyword(s):  
Conservation Laws ◽  
Low Energy ◽  
Energy Decomposition ◽  
Viscous Conservation Laws
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