Fractional derivatives of composite functions and the Cauchy problem for the nonlinear half wave equation

DOI10.1007/s00029-019-0460-4zbMath1428.35662arXiv1707.08319OpenAlexW2963998171WikidataQ128498975 ScholiaQ128498975MaRDI QIDQ1725966

Kunio Hidano, Chuanfang Wang

Publication date: 15 February 2019

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.08319

zbMATH Keywords

Strichartz estimatesGlassey conjecturefractional chain rulehalf wave equations

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Second-order nonlinear hyperbolic equations (35L70) Initial value problems for second-order hyperbolic equations (35L15) Initial value problems for nonlinear first-order PDEs (35F25) Fractional partial differential equations (35R11) Harmonic analysis and PDEs (42B37)

Related Items

Nondispersive solutions to the mass critical half-wave equation in two dimensions ⋮ Weighted fractional chain rule and nonlinear wave equations with minimal regularity ⋮ Concerning ill-posedness for semilinear wave equations ⋮ Blowup dynamics for mass critical half-wave equation in 3D ⋮ Lifespan estimates of 1D non-gauge invariant semilinear semirelativistic equations ⋮ Blow up for small-amplitude semilinear wave equations with mixed nonlinearities on asymptotically Euclidean manifolds ⋮ A special form of solution to half-wave equations

Cites Work

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• On the regularity of the flow map associated with the 1D cubic periodic half-wave equation.
• Global parametrices and dispersive estimates for variable coefficient wave equations
• On almost global existence and local well posedness for some 3-D quasi-linear wave equations
• Space-time \(L^2\)-estimates and life span of the Klainerman-Machedon radial solutions to some semi-linear wave equations.
• Morawetz-Strichartz estimates for spherically symmetric solutions to wave equations and applications to semilinear Cauchy problems.
• Blow-up of solutions to semilinear wave equations with variable coefficients and boundary
• The Glassey conjecture with radially symmetric data
• Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation
• A sharp counterexample to the local existence of low-regularity solutions to nonlinear wave equations
• Lectures on nonlinear hyperbolic differential equations
• Blow-up for self-interacting fractional Ginzburg-Landau equation
• On the Cauchy problem for the nonlinear semi-relativistic equation in Sobolev spaces
• Long time dynamics for semi-relativistic NLS and half wave in arbitrary dimension
• Almost global existence for some semilinear wave equations
• The analysis of linear partial differential operators. II: Differential operators with constant coefficients
• On nonlinear Schrödinger equations. II: \(H^ S\)-solutions and unconditional well-posedness
• Effective integrable dynamics for a certain nonlinear wave equation
• Weighted fractional chain rule and nonlinear wave equations with minimal regularity
• On global well-posedness for nonlinear semirelativistic equations in some scaling subcritical and critical cases
• The Glassey conjecture for nontrapping obstacles
• Finite time blow up for critical wave equations in high dimensions
• First and second order approximations for a nonlinear wave equation
• Nondispersive solutions to the \(L ^{2}\)-critical half-wave equation
• Some remarks on Strichartz estimates for the homogeneous wave equation
• The Strauss conjecture on Kerr black hole backgrounds
• Local well-posedness and ill-posedness on the equation of type \(\square u=u^k(\partial u)^\alpha\)
• Some nonexistence results for a semirelativistic Schrödinger equation with nongauge power type nonlinearity
• The Glassey conjecture on asymptotically flat manifolds
• Fourier Analysis and Nonlinear Partial Differential Equations
• Weighted Strichartz estimates with angular regularity and their applications
• Commutator estimates and the euler and navier-stokes equations
• A Semilinear Dirac Equation inH^s(R³) fors> 1
• Low Energy Scattering for Nonlinear Schrödinger Equations in Fractional Order Sobolev Spaces
• Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
• Ill-Posedness of the Cubic Nonlinear Half-Wave Equation and Other Fractional NLS on the Real Line
• Long-Time Existence of Quasilinear Wave Equations Exterior to Star-Shaped Obstacles via Energy Methods
• Blow up of solutions to the Cauchy problem for nonlinear wave equations