scholarly journals Loss of Regularity of Solutions of the Lighthill Problem for Shock Diffraction for Potential Flow

2020 ◽  
Vol 52 (2) ◽  
pp. 1096-1114 ◽  
Author(s):  
Gui-Qiang Chen ◽  
Mikhail Feldman ◽  
Jingchen Hu ◽  
Wei Xiang
Keyword(s):  
Potential Flow ◽  
Regularity Of Solutions ◽  
Shock Diffraction ◽  
Loss Of Regularity

scholarly journals Regularity of solutions to regular shock reflection for potential flow

2008 ◽  
Vol 175 (3) ◽  
pp. 505-543 ◽  
Author(s):  
Myoungjean Bae ◽  
Gui-Qiang Chen ◽  
Mikhail Feldman
Keyword(s):  
Potential Flow ◽  
Shock Reflection ◽  
Regularity Of Solutions

VISCOUS POTENTIAL FLOW ANALYSIS OF STRESS-INDUCED CAVITATION IN AN APERTURE FLOW

2006 ◽  
Vol 16 (7) ◽  
pp. 763-776 ◽  
Author(s):  
T. Funada ◽  
J. Wang ◽  
Daniel D. Joseph
Keyword(s):  
Potential Flow ◽  
Flow Analysis ◽  
Viscous Potential Flow

scholarly journals Diffeomorphism cocycles over partially hyperbolic systems

2020 ◽  
pp. 1-24
Author(s):  
VICTORIA SADOVSKAYA
Keyword(s):  
Hyperbolic System ◽  
Compact Manifold ◽  
Hyperbolic Systems ◽  
Riemannian Metrics ◽  
Hölder Continuous ◽  
Group Of Diffeomorphisms ◽  
Small Loss ◽  
Partially Hyperbolic ◽  
Loss Of Regularity

Abstract We consider Hölder continuous cocycles over an accessible partially hyperbolic system with values in the group of diffeomorphisms of a compact manifold $\mathcal {M}$ . We obtain several results for this setting. If a cocycle is bounded in $C^{1+\gamma }$ , we show that it has a continuous invariant family of $\gamma $ -Hölder Riemannian metrics on $\mathcal {M}$ . We establish continuity of a measurable conjugacy between two cocycles assuming bunching or existence of holonomies for both and pre-compactness in $C^0$ for one of them. We give conditions for existence of a continuous conjugacy between two cocycles in terms of their cycle weights. We also study the relation between the conjugacy and holonomies of the cocycles. Our results give arbitrarily small loss of regularity of the conjugacy along the fiber compared to that of the holonomies and of the cocycle.

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