18,840 research outputs found
The quintic nonlinear Schr\"odinger equation on three-dimensional Zoll manifolds
Let (M,g) be a three-dimensional smooth compact Riemannian manifold such that
all geodesics are simple and closed with a common minimal period, such as the
3-sphere S^3 with canonical metric. In this work the global well-posedness
problem for the quintic nonlinear Schr\"odinger equation i\partial_t u+\Delta
u=\pm|u|^4u, u|_{t=0}=u_0 is solved for small initial data u_0 in the energy
space H^1(M), which is the scaling-critical space. Further, local
well-posedness for large data, as well as persistence of higher initial Sobolev
regularity is obtained. This extends previous results of Burq-G\'erard-Tzvetkov
to the endpoint case
Harness for Vertically Supporting Slender Bodies for Vibration Testing
Support techniques for restraint of slender bodies such as launch vehicle
On the Cauchy problem for the derivative nonlinear Schroedinger equation with periodic boundary condition
It is shown that the Cauchy problem for the DNLS equation in the spatially
periodic setting is locally well-posed in Sobolev spaces H^s(T) for s \geq 1/2.
Moreover, global well-posedness is shown for s \geq 1 and data with small L^2
norm.Comment: 22 page
Trigonometric time integrators for the Zakharov system
The main challenge in the analysis of numerical schemes for the Zakharov
system originates from the presence of derivatives in the nonlinearity. In this
paper a new trigonometric time-integration scheme for the Zakharov system is
constructed and convergence is proved. The time-step restriction is independent
from a spatial discretization. Numerical experiments confirm the findings
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