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Title of Journal: Arch Rational Mech Anal

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Abbravation: Archive for Rational Mechanics and Analysis

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Springer Berlin Heidelberg

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10.1007/bf02806902

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1432-0673

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Counterexamples to the Sonic Criterion

Authors: Volker Elling
Publish Date: 2008/11/28
Volume: 194, Issue: 3, Pages: 987-1010
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Abstract

We consider selfsimilar pseudosteady shock reflection at an oblique wall There are three parameters wall corner angle Mach number angle of incident shock Ever since Ernst Mach discovered the irregular reflection named after him researchers have sought to predict precisely for which parameters the reflection is regular Three conflicting proposals—the detachment sonic and von Neumann criteria—have been studied extensively without a clear result We demonstrate that the sonic criterion is not correct We consider polytropic potential flow and prove that there is an open nonempty set of parameters that admit a global regular reflection with a reflected shock that is transonic We also provide a clear physical reason the flow type sub or supersonic is not decisive instead the reflected shock type weak or strong determines whether structural perturbations decay towards the reflection point

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Other Papers In This Journal:
  1. Optimal Design in Conductivity Under Locally Constrained Heat Flux
  2. Regularity Issues in the Problem of Fluid Structure Interaction
  3. Negative Eigenvalues of Two-Dimensional Schrödinger Operators
  4. Dobrushin States in the $${\phi^4_1}$$ Model
  5. The Liouville Theorem and the L 2 Decay for the FENE Dumbbell Model of Polymeric Flows
  6. The Liouville Theorem and the L 2 Decay for the FENE Dumbbell Model of Polymeric Flows
  7. Dislocation Dynamics: Short-time Existence and Uniqueness of the Solution
  8. On Nonlinear Stochastic Balance Laws
  9. Weak Solutions of the Navier–Stokes Equations for Compressible Flows in a Half-Space with No-Slip Boundary Conditions
  10. Generalized Transition Fronts for One-Dimensional Almost Periodic Fisher-KPP Equations
  11. The Gel’fand Problem for the Biharmonic Operator
  12. The Existence Problem for Steiner Networks in Strictly Convex Domains
  13. Stability of Detonation Profiles in the ZND Limit
  14. Uniqueness of Absolute Minimizers for $${L^\infty}$$-Functionals Involving Hamiltonians $${H(x,p)}$$H(x,p)
  15. A Condition for the Hölder Regularity of Local Minimizers of a Nonlinear Elastic Energy in Two Dimensions
  16. Kinetic Stabilization¶of a Nonlinear Sonic Phase Boundary
  17. The Toda System and Clustering Interfaces in the Allen–Cahn equation
  18. A Stability Criterion for Two-Fluid Interfaces and Applications
  19. Long-Time Convergence of an Adaptive Biasing Force Method: The Bi-Channel Case
  20. Displacement Convexity and Minimal Fronts at Phase Boundaries
  21. Gradient Bounds for Elliptic Problems Singular at the Boundary
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