201 research outputs found
A threshold phenomenon for embeddings of into Orlicz spaces
We consider a sequence of positive smooth critical points of the
Adams-Moser-Trudinger embedding of into Orlicz spaces. We study its
concentration-compactness behavior and show that if the sequence is not
precompact, then the liminf of the -norms of the functions is greater
than or equal to a positive geometric constant.Comment: 14 Page
Multiple solutions of the quasirelativistic Choquard equation
We prove existence of multiple solutions to the quasirelativistic Choquard equation with a scalar potential
On Singularity formation for the L^2-critical Boson star equation
We prove a general, non-perturbative result about finite-time blowup
solutions for the -critical boson star equation in 3 space dimensions. Under
the sole assumption that the solution blows up in at finite time, we
show that has a unique weak limit in and that has a
unique weak limit in the sense of measures. Moreover, we prove that the
limiting measure exhibits minimal mass concentration. A central ingredient used
in the proof is a "finite speed of propagation" property, which puts a strong
rigidity on the blowup behavior of .
As the second main result, we prove that any radial finite-time blowup
solution converges strongly in away from the origin. For radial
solutions, this result establishes a large data blowup conjecture for the
-critical boson star equation, similar to a conjecture which was
originally formulated by F. Merle and P. Raphael for the -critical
nonlinear Schr\"odinger equation in [CMP 253 (2005), 675-704].
We also discuss some extensions of our results to other -critical
theories of gravitational collapse, in particular to critical Hartree-type
equations.Comment: 24 pages. Accepted in Nonlinearit
Analysis of Nematic Liquid Crystals with Disclination Lines
We investigate the structure of nematic liquid crystal thin films described
by the Landau--de Gennes tensor-valued order parameter with Dirichlet boundary
conditions of nonzero degree. We prove that as the elasticity constant goes to
zero a limiting uniaxial texture forms with disclination lines corresponding to
a finite number of defects, all of degree 1/2 or all of degree -1/2. We also
state a result on the limiting behavior of minimizers of the Chern-Simons-Higgs
model without magnetic field that follows from a similar proof.Comment: 40 pages, 1 figur
Lifespan theorem for constrained surface diffusion flows
We consider closed immersed hypersurfaces in and evolving by
a class of constrained surface diffusion flows. Our result, similar to earlier
results for the Willmore flow, gives both a positive lower bound on the time
for which a smooth solution exists, and a small upper bound on a power of the
total curvature during this time. By phrasing the theorem in terms of the
concentration of curvature in the initial surface, our result holds for very
general initial data and has applications to further development in asymptotic
analysis for these flows.Comment: 29 pages. arXiv admin note: substantial text overlap with
arXiv:1201.657
Green's functions for parabolic systems of second order in time-varying domains
We construct Green's functions for divergence form, second order parabolic
systems in non-smooth time-varying domains whose boundaries are locally
represented as graph of functions that are Lipschitz continuous in the spatial
variables and 1/2-H\"older continuous in the time variable, under the
assumption that weak solutions of the system satisfy an interior H\"older
continuity estimate. We also derive global pointwise estimates for Green's
function in such time-varying domains under the assumption that weak solutions
of the system vanishing on a portion of the boundary satisfy a certain local
boundedness estimate and a local H\"older continuity estimate. In particular,
our results apply to complex perturbations of a single real equation.Comment: 25 pages, 0 figur
An improved geometric inequality via vanishing moments, with applications to singular Liouville equations
We consider a class of singular Liouville equations on compact surfaces
motivated by the study of Electroweak and Self-Dual Chern-Simons theories, the
Gaussian curvature prescription with conical singularities and Onsager's
description of turbulence. We analyse the problem of existence variationally,
and show how the angular distribution of the conformal volume near the
singularities may lead to improvements in the Moser-Trudinger inequality, and
in turn to lower bounds on the Euler-Lagrange functional. We then discuss
existence and non-existence results.Comment: some references adde
Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations
We present new interior regularity criteria for suitable weak solutions of
the 3-D Navier-Stokes equations: a suitable weak solution is regular near an
interior point if either the scaled -norm of the velocity
with , , or the -norm of the
vorticity with , , or the
-norm of the gradient of the vorticity with , , , is sufficiently small near
Global compactness results for nonlocal problems
International audienceWe obtain a Struwe type global compactness result for a class of nonlinear nonlocal problems involving the fractional Laplacian operator and nonlinearities at critical growth
Code assessment and modelling for Design Basis Accident analysis of the European Sodium Fast Reactor design. Part II: Optimised core and representative transients analysis
The new reactor concepts proposed in the Generation IV International Forum require the development and validation of computational tools able to assess their safety performance. In the first part of this paper the models of the ESFR design developed by several organisations in the framework of the CP-ESFR project were presented and their reliability validated via a benchmarking exercise. This second part of the paper includes the application of those tools for the analysis of design basis accident (DBC) scenarios of the reference design. Further, this paper also introduces the main features of the core optimisation process carried out within the project with the objective to enhance the core safety performance through the reduction of the positive coolant density reactivity effect. The influence of this optimised core design on the reactor safety performance during the previously analysed transients is also discussed. The conclusion provides an overview of the work performed by the partners involved in the project towards the development and enhancement of computational tools specifically tailored to the evaluation of the safety performance of the Generation IV innovative nuclear reactor designs
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