The mathematical approach to the sonic barrier

DOI10.1090/S0273-0979-1982-14965-5zbMath0506.76064WikidataQ56483859 ScholiaQ56483859MaRDI QIDQ4743948

Cathleen Synge Morawetz

Publication date: 1982

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

artificial viscosityBibliographyentropy conditionTricomi equationtransonic controversyimproperly posedlinear equations of mixed typeelliptic and hyperbolic quasi-linear differential equationsLavrent'ev-Bitsadze casemultiplier method of Friedrichsprofile computationshockless transition from local supersonic backwards to subsonic

Mathematics Subject Classification ID

Transonic flows (76H05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Perturbations in context of PDEs (35B20) Research exposition (monographs, survey articles) pertaining to fluid mechanics (76-02) Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing (76B10) History of fluid mechanics (76-03)

Related Items

Finite time blow-up for a semilinear generalized Tricomi system with mixed nonlinearity ⋮ On two-dimensional sonic-subsonic flow ⋮ Commentary: Three decades after Cathleen Synge Morawetz’s paper “The mathematical approach to the sonic barrier” ⋮ The self-similar solutions of the one-dimensional semilinear Tricomi-type equations ⋮ Morawetz’s contributions to the mathematical theory of transonic flows, shock waves, and partial differential equations of mixed type ⋮ Global existence for the one-dimensional second order semilinear hyperbolic equations ⋮ Integral Transform Approach to Time-Dependent Partial Differential Equations ⋮ Vanishing viscosity method for transonic flow ⋮ Integral transform approach to generalized Tricomi equations ⋮ Global Existence for then-Dimensional Semilinear Tricomi-Type Equations ⋮ SELF-SIMILAR ISOTHERMAL IRROTATIONAL MOTION FOR THE EULER, EULER–POISSON SYSTEMS AND THE FORMATION OF THE PLASMA SHEATH ⋮ Hadamard's example and solvability of the mixed Cauchy problem for the multidimensional Gellerstedt equation

Cites Work

• The hodograph method in fluid-dynamics in the light of variational inequalities
• Systems of conservation laws of mixed type
• A theory of supercritical wing sections, with computer programs and examples
• On the non-existence of continuous transonic flows past profiles I
• A weak solution for a system of equations of elliptic-hyperbolic type
• Symmetric positive linear differential equations
• Stable and Entropy Satisfying Approximations for Transonic Flow Calculations
• Shock-Free Wing Design
• Design of supercritical swept wings
• Iterative solution of transonic flows over airfoils and wings, including flows at mach 1
• Implicit Finite-Difference Computations of Unsteady Transonic Flows about Airfoils
• The dirichlet problem for the tricomi equation
• Calculation of plane steady transonic flows
• Exakte Lösungen der Differentialgleichungen einer adiabatischen Gasströmung
• The engineer grapples with nonlinear problems
• Flow of a compressible fluid about a cylinder
• ON THE HODOGRAPH TRANSFORMATION FOR HIGH-SPEED FLOW: II. A FLOW WITH CIRCULATION
• On the Presence of Shocks in Mixed Subsonic-Supersonic Flow Patterns
• Existence and uniqueness of a subsonic flow past a given profile
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item