Finite-time degeneration of hyperbolicity without blowup for quasilinear wave equations (Q2402625)

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English	Finite-time degeneration of hyperbolicity without blowup for quasilinear wave equations	scientific article

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title

Finite-time degeneration of hyperbolicity without blowup for quasilinear wave equations (English)

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zbMATH Open document ID

1382.35168

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DOI

10.2140/apde.2017.10.2001

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12 September 2017

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full work available at URL

https://arxiv.org/abs/1610.00821

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Mathematics Subject Classification ID

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degenerate hyperbolic

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strictly hyperbolic

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Tricomi equation

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weakly hyperbolic

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three spatial dimensions

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MaRDI profile type

MaRDI publication profile

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Blowup of small data solutions for a quasilinear wave equation in two space dimensions.

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Blowup of small data solutions for a class of quasilinear wave equations in two space dimensions. II

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The null condition for quasilinear wave equations in two space dimensions, II

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Q3922967

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Branching of singularities for degenerate hyperbolic operators and Stokes phenomena. II

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Branching of singularities for degenerate hyperbolic operator and Stokes phenomena. III

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Branching of singularities for degenerate hyperbolic operator and Stokes phenomena. IV

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Branching of singularities for degenerate hyperbolic operators

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A degenerate hyperbolic equation under Levi conditions

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Well posedness under Levi conditions for a degenerate second order Cauchy problem

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The formation of shocks in 3-dimensional fluids.

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Shock development in spherical symmetry

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Compressible Flow and Euler's Equations

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An example of a weakly hyperbolic Cauchy problem not well posed in \(C^\infty\)

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On the spectral properties ofL±in three dimensions

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Well-posedness in smooth function spaces for moving-boundary 1-D compressible euler equations in physical vacuum

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Well-posedness in smooth function spaces for the moving-boundary three-dimensional compressible Euler equations in physical vacuum

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A priori estimates for the free-boundary 3D compressible Euler equations in physical vacuum

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Well posedness in \(C^ \infty\) for a weakly hyperbolic second order equation

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Global solvability for the degenerate Kirchhoff equation with real analytic data

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ON THE LOCAL SOLVABILITY FOR A NONLINEAR WEAKLY HYPERBOLIC EQUATION WITH ANALYTIC COEFFICIENTS

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Blowup of classical solutions for a class of 3-D quasilinear wave equations with small initial data.

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On the lifespan and the blowup mechanism of smooth solutions to a class of 2-D nonlinear wave equations with small initial data

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Blowup time and blowup mechanism of small data solutions to general 2-D quasilinear wave equations

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Nonlinear Stability of Self-Similar Solutions for Semilinear Wave Equations

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Nonscattering solutions and blowup at infinity for the critical wave equation

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Stable blow up dynamics for energy supercritical wave equations

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Exotic blowup solutions for the \(u^5\) focusing wave equation in \(\mathbb{R}^{3}\)

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Universality of the blow-up profile for small type II blow-up solutions of the energy-critical wave equation: the nonradial case

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Q3728516

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Local solutions for a nonlinear degenerate Hyperbolic equation

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The inverse function theorem of Nash and Moser

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Energy estimates for a class of degenerate hyperbolic equations

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Degenerate hyperbolic equations with lower degree degeneracy

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Local isometric embedding of surfaces with nonpositive Gaussian curvature.

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On the Cauchy problem of degenerate hyperbolic equations

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H ∞ Well-Posedness for Degenerate p-Evolution Models of Higher Order with Time-Dependent Coefficients

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Small-data shock formation in solutions to 3D quasilinear wave equations: An overview

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Lectures on nonlinear hyperbolic differential equations

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On a sharp Levi condition in Gevrey classes for some infinitely degenerate hyperbolic equations and its necessity

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Well-posedness for compressible Euler equations with physical vacuum singularity

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Vacuum in Gas and Fluid Dynamics

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Formation of singularities in one-dimensional nonlinear wave propagation

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Blow-up for quasi-linear wave equations in three space dimensions

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BLOW UP OF SOLUTIONS TO THE SECOND SOUND EQUATION IN ONE SPACE DIMENSION

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Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation

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Blowup behaviour for the nonlinear Klein-Gordon equation

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Formation of singularities for wave equations including the nonlinear vibrating string

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Full range of blow up exponents for the quintic wave equation in three dimensions

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Renormalization and blow up for charge one equivariant critical wave maps

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Slow blow-up solutions for the \(H^1(\mathbb R^3)\) critical focusing semilinear wave equation

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Global dynamics away from the ground state for the energy-critical nonlinear wave equation

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Global dynamics of the nonradial energy-critical wave equation above the ground state energy

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Threshold phenomenon for the quintic wave equation in three dimensions

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Center-stable manifold of the ground state in the energy space for the critical wave equation

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Hyperbolic systems of conservation laws II

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Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the Form Pu tt = -Au + ℱ(u)

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Counterexamples to local existence for quasilinear wave equations

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Global solutions of quasilinear wave equations

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Local solvability in c∞for quasi-linear weakly hyperbolic equations of second order

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Well posedness in the C∞ class for utt=a(u)Δu

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Analysis - 10

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Global dynamics above the ground state energy for the focusing nonlinear Klein-Gordon equation

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Invariant manifolds and dispersive Hamiltonian evolution equations

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Global dynamics above the ground state for the nonlinear Klein-Gordon equation without a radial assumption

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Invariant Manifolds Around Soliton Manifolds for the Nonlinear Klein–Gordon Equation

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The cauchy problem for weakly hyperbolic equations of second order

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A necessary and sufficient condition for the hyperbolicity of second order equations with two independent variables

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Saddle points and instability of nonlinear hyperbolic equations

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Stable blow up dynamics for the critical co-rotational wave maps and equivariant Yang-Mills problems

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On the formation of singularities in the critical \(O(3)\) \(\sigma \)-model

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On the existence and cusp singularity of solutions to semilinear generalized Tricomi equations with discontinuous initial data

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On the existence of low regularity solutions to semilinear generalized Tricomi equations in mixed type domains

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Tricomi type equations with terms of lower order

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Formation of singularities in three-dimensional compressible fluids

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Shock Formation in Small-Data Solutions to 3D Quasilinear Wave Equations

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Stable shock formation for nearly simple outgoing plane symmetric waves

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Equivariant wave maps in two space dimensions

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Global existence of solutions to some quasilinear wave equation in one space dimension.

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Degeneracy in Finite Time of 1D Quasilinear Wave Equations

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Mathematics(1 entry)

mardi Publication:2402625