Strichartz estimates and maximal operators for the wave equation in R3
Marius Beceanu,Michael Goldberg +1 more
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TLDR
In this article, the authors prove sharp Strichartz-type estimates in three dimensions, including some which hold in reverse space-time norms, for the wave equation with potential, for small initial data of semilinear wave equations in R 3 with quintic or higher monomial nonlinearities.About:
This article is published in Journal of Functional Analysis.The article was published on 2014-02-01 and is currently open access. It has received 39 citations till now. The article focuses on the topics: Maximal function & Wave equation.read more
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Dispersive Estimates for Four Dimensional Schrödinger and Wave Equations with Obstructions at Zero Energy
TL;DR: In this article, the Schrodinger operator H = − Δ + V when there are obstructions, a resonance or an eigenvalue, at zero energy, and it was shown that H = 0.
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Strichartz estimates in similarity coordinates and stable blowup for the critical wave equation
TL;DR: In this article, the authors established Strichartz estimates in similarity coordinates for the radial wave equation in three spatial dimensions with a (time-dependent) self-similar potential and proved the asymptotic stability of the ODE blowup profile in the energy space.
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Strichartz estimates in similarity coordinates and stable blowup for the critical wave equation
TL;DR: In this article, the authors established Strichartz estimates in similarity coordinates for the radial wave equation in three spatial dimensions with a time-dependent self-similar potential, and proved the asymptotic stability of the ordinary differential equations blowup profile in the energy space.
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Attractors of Hamilton nonlinear PDEs
TL;DR: In this paper, a survey of long time behavior and attractors for Hamiltonian nonlinear partial differential equations, considering the global attraction to stationary states, stationary orbits, and solitons, is presented.
Journal ArticleDOI
Dispersive estimates for four dimensional Schr\"{o}dinger and wave equations with obstructions at zero energy
TL;DR: In this paper, the Schrodinger operator with potential at zero energy was studied and it was shown that if there is a resonance or an eigenvalue at zero-energy, then there exists a time dependent, finite rank operator (F_t) satisfying the following conditions:
References
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Endpoint Strichartz estimates
Markus Keel,Terence Tao +1 more
TL;DR: In this paper, an abstract Strichartz estimate for the wave equation (in dimension n ≥ 4) and for the Schrodinger equation (n ≥ 3) was proved.
Proceedings Article
Harmonic analysis
TL;DR: A method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms, of a signal having an arbitrary dimension of the digital representation by reducing the transform to a vector-to-circulant matrix multiplying.
Journal Article
Oscillatory integrals and regularity of dispersive equations
TL;DR: In this article, the authors studied the relationship between local and global smoothing properties of dispersive equations and their application to nonlinear problems and their link with restriction theorems for the Fourier transform and pointwise convergence results.
Journal ArticleDOI
Well-posedness of the initial value problem for the Korteweg-de Vries equation
TL;DR: In this paper, the authors studied the local and global well-posedness of the IVP (1.1) in classical Sobolev spaces Hs(R) and showed that the global wellposedness depends on the available local theory and on the conservation laws satisfied by solutions of (1).
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