2016, Mathematical surveys and monographs, ISBN 1470428571, Volume 214, xxiii, 515 pages

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

Analysis and PDE, ISSN 2157-5045, 2017, Volume 10, Issue 8, pp. 2001 - 2030

In three spatial dimensions, we study the Cauchy problem for the wave equation -partial derivative(2)(t)Psi + (1 + Psi)(P) Delta Psi = 0 for P epsilon {1, 2}....

Strictly hyperbolic | Weakly hyperbolic | Degenerate hyperbolic | Tricomi equation | MATHEMATICS, APPLIED | KLEIN-GORDON EQUATION | strictly hyperbolic | GROUND-STATE | degenerate hyperbolic | CAUCHY-PROBLEM | WELL-POSEDNESS | C-INFINITY | 2 SPACE DIMENSIONS | MATHEMATICS | COMPRESSIBLE EULER EQUATIONS | STOKES PHENOMENA | GLOBAL DYNAMICS | SMALL INITIAL DATA | weakly hyperbolic | Mathematics - Analysis of PDEs

Strictly hyperbolic | Weakly hyperbolic | Degenerate hyperbolic | Tricomi equation | MATHEMATICS, APPLIED | KLEIN-GORDON EQUATION | strictly hyperbolic | GROUND-STATE | degenerate hyperbolic | CAUCHY-PROBLEM | WELL-POSEDNESS | C-INFINITY | 2 SPACE DIMENSIONS | MATHEMATICS | COMPRESSIBLE EULER EQUATIONS | STOKES PHENOMENA | GLOBAL DYNAMICS | SMALL INITIAL DATA | weakly hyperbolic | Mathematics - Analysis of PDEs

Journal Article

Analysis and PDE, ISSN 2157-5045, 2014, Volume 7, Issue 4, pp. 771 - 901

We study the coupling of the Einstein field equations of general relativity to a family of nonlinear electromagnetic field equations. The family comprises all...

Weak null condition | Energy currents | Nonlinear electromagnetism | Vector field method | Hardy inequality | Born-infeld | Lagrangian field theory | Klainerman-Sobolev inequality | Regularly hyperbolic | Quasilinear wave equation | Null condition | Global existence | Null decomposition | Canonical stress | EXISTENCE | VACUUM | MATHEMATICS, APPLIED | ELECTROMAGNETIC-FIELD THEORY | regularly hyperbolic | PROOF | EULER-NORDSTROM SYSTEM | energy currents | quasilinear wave equation | MATHEMATICS | Born-Infeld | null condition | global existence | MAXWELL-EQUATIONS | nonlinear electromagnetism | null decomposition | canonical stress | vector field method | weak null condition

Weak null condition | Energy currents | Nonlinear electromagnetism | Vector field method | Hardy inequality | Born-infeld | Lagrangian field theory | Klainerman-Sobolev inequality | Regularly hyperbolic | Quasilinear wave equation | Null condition | Global existence | Null decomposition | Canonical stress | EXISTENCE | VACUUM | MATHEMATICS, APPLIED | ELECTROMAGNETIC-FIELD THEORY | regularly hyperbolic | PROOF | EULER-NORDSTROM SYSTEM | energy currents | quasilinear wave equation | MATHEMATICS | Born-Infeld | null condition | global existence | MAXWELL-EQUATIONS | nonlinear electromagnetism | null decomposition | canonical stress | vector field method | weak null condition

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 5/2011, Volume 304, Issue 1, pp. 229 - 280

We study the local-in-time hydrodynamic limit of the relativistic Boltzmann equation using a Hilbert expansion. More specifically, we prove the existence of...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | EXISTENCE | MECHANICS | KINETIC-EQUATIONS | EXPONENTIAL DECAY | NAVIER-STOKES | EULER-NORDSTROM SYSTEM | ASYMPTOTIC STABILITY | DYNAMIC LIMITS | PHYSICS, MATHEMATICAL | Universities and colleges

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | EXISTENCE | MECHANICS | KINETIC-EQUATIONS | EXPONENTIAL DECAY | NAVIER-STOKES | EULER-NORDSTROM SYSTEM | ASYMPTOTIC STABILITY | DYNAMIC LIMITS | PHYSICS, MATHEMATICAL | Universities and colleges

Journal Article

Annals of PDE, ISSN 2524-5317, 6/2018, Volume 4, Issue 1, pp. 1 - 131

We prove a stable shock formation result for a large class of systems of quasilinear wave equations in two spatial dimensions. We give a precise description of...

35L52 | 35L72 | Primary 35L67 | Vectorfield method | Physics | Wave breaking | Eikonal function | Strong null condition | Mathematical Methods in Physics | Characteristics | Secondary 35L05 | Eikonal equation | Null condition | Null hypersurface | Singularity formation | Genuinely nonlinear strictly hyperbolic systems | Partial Differential Equations

35L52 | 35L72 | Primary 35L67 | Vectorfield method | Physics | Wave breaking | Eikonal function | Strong null condition | Mathematical Methods in Physics | Characteristics | Secondary 35L05 | Eikonal equation | Null condition | Null hypersurface | Singularity formation | Genuinely nonlinear strictly hyperbolic systems | Partial Differential Equations

Journal Article

Annals of PDE, ISSN 2199-2576, 12/2016, Volume 2, Issue 2, pp. 1 - 198

In an influential 1964 article, P. Lax studied $$2 \times 2$$ 2 × 2 genuinely nonlinear strictly hyperbolic PDE systems (in one spatial dimension). Using the...

35L72 | Vectorfield method | 35Q31 | Physics | Wave breaking | 35L10 | 76N10 | Eikonal function | Primary: 35L67 | Mathematical Methods in Physics | Characteristics | Secondary: 35L05 | Eikonal equation | Null hypersurface | Singularity formation | Genuinely nonlinear strictly hyperbolic systems | Partial Differential Equations

35L72 | Vectorfield method | 35Q31 | Physics | Wave breaking | 35L10 | 76N10 | Eikonal function | Primary: 35L67 | Mathematical Methods in Physics | Characteristics | Secondary: 35L05 | Eikonal equation | Null hypersurface | Singularity formation | Genuinely nonlinear strictly hyperbolic systems | Partial Differential Equations

Journal Article

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