2,677,702 research outputs found
Maximizers for the Strichartz Inequalities for the Wave Equation
We prove the existence of maximizers for Strichartz inequalities for the wave
equation in dimensions . Our approach follows the scheme given by
Shao, which obtains the existence of maximizers in the context of the
Schr\"odinger equation. The main tool that we use is the linear profile
decomposition for the wave equation which we prove in , , extending the profile decomposition result of Bahouri and Gerard,
previously obtained in .Comment: 28 pages, revised version, minor change
Brane-induced Skyrmions: Baryons in Holographic QCD
We study baryons in holographic QCD with multi brane
system. In holographic QCD, the baryon appears as a topologically non-trivial
chiral soliton in a four-dimensional effective theory of mesons, which is
called `Brane-induced Skyrmion'. We derive and calculate the Euler-Lagrange
equation for the hedgehog configuration with chiral profile and
-meson profile , and obtain the soliton solution of the
holographic QCD.Comment: 5 pages, 6 figure
Many-Body Theory of Synchronization by Long-Range Interactions
Synchronization of coupled oscillators on a -dimensional lattice with the
power-law coupling and randomly distributed intrinsic
frequency is analyzed. A systematic perturbation theory is developed to
calculate the order parameter profile and correlation functions in powers of
. For , the system exhibits a sharp
synchronization transition as described by the conventional mean-field theory.
For , the transition is smeared by the quenched disorder, and the
macroscopic order parameter \Av\psi decays slowly with as |\Av\psi|
\propto g_0^2.Comment: 4 pages, 2 figure
On Traveling Solitary Waves and Absence of Small Data Scattering for Nonlinear Half-Wave Equations
We consider nonlinear half-wave equations with focusing power-type
nonlinearity i \pt_t u = \sqrt{-\Delta} \, u - |u|^{p-1} u, \quad \mbox{with
$(t,x) \in \R \times \R^d$} with exponents for and for . We study traveling solitary waves of the
form with frequency ,
velocity , and some finite-energy profile ,
. We prove that traveling solitary waves for speeds do not exist. Furthermore, we generalize the non-existence result to
the square root Klein--Gordon operator \sqrt{-\DD+m^2} and other
nonlinearities.
As a second main result, we show that small data scattering fails to hold for
the focusing half-wave equation in any space dimension. The proof is based on
the existence and properties of traveling solitary waves for speeds .
Finally, we discuss the energy-critical case when in dimensions
.Comment: 17 page
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