scientific article; zbMATH DE number 5222459
From MaRDI portal
Publication:5432012
zbMath1138.35060MaRDI QIDQ5432012
Publication date: 2 January 2008
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shocks and singularities for hyperbolic equations (35L67) Shock waves and blast waves in fluid mechanics (76L05) Gas dynamics (general theory) (76N15) Second-order nonlinear hyperbolic equations (35L70) Hyperbolic conservation laws (35L65) Quantum hydrodynamics and relativistic hydrodynamics (76Y05) Hyperbolic equations on manifolds (58J45)
Related Items (65)
On the development of shocks in fluids ⋮ Stable big bang formation in near-FLRW solutions to the Einstein-scalar field and Einstein-stiff fluid systems ⋮ The maximal development of near-FLRW data for the Einstein-scalar field system with spatial topology \(\mathbb{S}^3\) ⋮ Global solutions of the Euler-Maxwell two-fluid system in 3D ⋮ Blow-up of waves on singular spacetimes with generic spatial metrics ⋮ Expanding large global solutions of the equations of compressible fluid mechanics ⋮ Blow up of solutions to 1-d Euler equations with time-dependent damping ⋮ Completely linear degeneracy for quasilinear hyperbolic systems ⋮ Decay of the Weyl curvature in expanding black hole cosmologies ⋮ Global nonlinear stability of large dispersive solutions to the Einstein equations ⋮ Nonresonant bilinear forms for partially dissipative hyperbolic systems violating the Shizuta-Kawashima condition ⋮ Formation and Construction of a Multidimensional Shock Wave for the First-Order Hyperbolic Conservation Law with Smooth Initial Data ⋮ Rotating elastic string loops in flat and black hole spacetimes: stability, cosmic censorship and the Penrose process ⋮ Regularity for the Boltzmann equation conditional to macroscopic bounds ⋮ Formation of singularities for the relativistic Euler equations ⋮ Exact solutions and singularities of an X-point collapse in Hall magnetohydrodynamics ⋮ Predictability of subluminal and superluminal wave equations ⋮ Global smooth axisymmetric solutions to 2D compressible Euler equations of Chaplygin gases with non-zero vorticity ⋮ On the stability of relativistic perfect fluids with linear equations of state \(p=K\rho\) where \(1/3<K<1\) ⋮ The inviscid limit of viscous Burgers at nondegenerate shock formation ⋮ Optimal Decay Rates of the Compressible Euler Equations with Time-Dependent Damping in \({\mathbb {R}}^n\): (II) Overdamping Case ⋮ Breakdown of smooth solutions to the Müller-Israel-Stewart equations of relativistic viscous fluids ⋮ On ``hard stars in general relativity ⋮ The relativistic Euler equations: remarkable null structures and regularity properties ⋮ A priori estimates for a relativistic liquid with free surface boundary ⋮ NON-STATIONARY THERMO-DIFFUSION PROCESSES IN FINITE ONE-DIMENSIONAL CRYSTAL ⋮ Long time existence of smooth solutions to 2D compressible Euler equations of Chaplygin gases with non-zero vorticity ⋮ The relativistic Euler equations: ESI notes on their geo-analytic structures and implications for shocks in 1D and multi-dimensions ⋮ On the exterior stability of nonlinear wave equations ⋮ GLOBAL NEARLY-PLANE-SYMMETRIC SOLUTIONS TO THE MEMBRANE EQUATION ⋮ The hidden null structure of the compressible Euler equations and a prelude to applications ⋮ Blowup for projected 2-dimensional \(C^2\) solutions of compressible Euler equations with Coriolis force ⋮ Smooth solution of multi-dimensional nonhomogeneous conservation law: its formula, and necessary and sufficient blowup criterion ⋮ Formation and propagation of singularities in one-dimensional Chaplygin gas ⋮ Global existence and convergence to the modified Barenblatt solution for the compressible Euler equations with physical vacuum and time-dependent damping ⋮ Continued gravitational collapse for Newtonian stars ⋮ Stability of smooth solutions for the compressible Euler equations with time-dependent damping and one-side physical vacuum ⋮ Formation of finite-time singularities for nonlinear hyperbolic systems with small initial disturbances ⋮ The global supersonic flow with vacuum state in a 2D convex duct ⋮ Nonlinear stability of relativistic vortex sheets in three-dimensional Minkowski spacetime ⋮ Local well-posedness in Sobolev spaces for first-order barotropic causal relativistic viscous hydrodynamics ⋮ On global smooth solutions of 3-D compressible Euler equations with vanishing density in infinitely expanding balls ⋮ Self-similar solutions to the compressible Euler equations and their instabilities ⋮ Local existence and uniqueness in Sobolev spaces for first-order conformal causal relativistic viscous hydrodynamics ⋮ Blowup of smooth solutions of a class of complex conservation laws ⋮ Blowup for projected 2-dimensional rotational \(\mathrm{C}^2\) solutions of compressible Euler equations ⋮ The Euler Equations of Compressible Fluid Flow ⋮ The stabilizing effect of spacetime expansion on relativistic fluids with sharp results for the radiation equation of state ⋮ Small-data shock formation in solutions to 3D quasilinear wave equations: An overview ⋮ Shock formation in solutions to the \(2D\) compressible Euler equations in the presence of non-zero vorticity ⋮ The global smooth symmetric solution to 2-D full compressible Euler system of Chaplygin gases ⋮ Shock wave interactions and the Riemann-flat condition: the geometry behind metric smoothing and the existence of locally inertial frames in general relativity ⋮ On global axisymmetric solutions to 2D compressible full Euler equations of Chaplygin gases ⋮ Three-Dimensional Global Supersonic Euler Flows in the Infinitely Long Divergent Nozzles ⋮ Global smooth solutions to 3D irrotational Euler equations for Chaplygin gases ⋮ A priori estimates for solutions to the relativistic Euler equations with a moving vacuum boundary ⋮ Formation of unstable shocks for 2D isentropic compressible Euler ⋮ Rough sound waves in \(3D\) compressible Euler flow with vorticity ⋮ Decay and subluminality of modes of all wave numbers in the relativistic dynamics of viscous and heat conductive fluids ⋮ On a viable first-order formulation of relativistic viscous fluids and its applications to cosmology ⋮ Global stability for nonlinear wave equations with multi-localized initial data ⋮ Future Global Stability for Relativistic Perfect Fluids with Linear Equations of State $p=K\rho$ where $1/3<K<1/2$ ⋮ Global existence and asymptotic behavior of solutions to the Euler equations with time-dependent damping ⋮ The shock formation and optimal regularities of the resulting shock curves for 1D scalar conservation laws* ⋮ Local existence with low regularity for the 2D compressible Euler equations
This page was built for publication:
