Zobrazeno 1 - 10
of 220
pro vyhledávání: '"Burq, Nicolas"'
Autor:
Burq, Nicolas, Letrouit, Cyril
We prove delocalization of eigenvectors of vertex-transitive graphs via elementary estimates of the spectral projector. We recover in this way known results which were formerly proved using representation theory.Similar techniques show that for gener
Externí odkaz:
http://arxiv.org/abs/2407.12384
Nonnegative measures that are solutions to a transport equation with continuous coefficients have been widely studied. Because of the low regularity of the associated vector field, there is no natural flow since nonuniqueness of integral curves is th
Externí odkaz:
http://arxiv.org/abs/2407.02259
The celebrated geometric control condition of Bardos, Lebeau, and Rauch is necessary and sufficient for wave observability [1,7] and exact controllability. It requires that any point in phase-space be transported by the generalized geodesic flow to t
Externí odkaz:
http://arxiv.org/abs/2407.02255
We consider cubic NLS in dimensions 2, 3, 4 and we prove that almost surely solutions with randomized initial data at low regularity scatter. Moreover, we establish some smoothing properties of the associated scattering operator and precise the rate
Externí odkaz:
http://arxiv.org/abs/2406.07713
We consider the Wick ordered cubic Schr\"odinger equation (NLS) posed on the two-dimensional sphere, with initial data distributed according to a Gaussian measure. We show that the second Picard iteration does not improve the regularity of the initia
Externí odkaz:
http://arxiv.org/abs/2404.18241
We establish the probabilistic well-posedness of the nonlinear Schr\"odinger equation on the $2d$ sphere $\mathbb{S}^{2}$. The initial data are distributed according to Gaussian measures with typical regularity $H^{s}(\mathbb{S}^{2})$, for $s>0$. Thi
Externí odkaz:
http://arxiv.org/abs/2404.18229
Autor:
Burq, Nicolas, Zuily, Claude
We prove the sharp domain of dependence property for solutions to subelliptic wave equations for sums of squares of vector fields satisfying H\"ormander bracket condition. We deduce a unique continuation property for the square root of subelliptic La
Externí odkaz:
http://arxiv.org/abs/2309.05992
For the wave and the Schr\"odinger equations we show how observability can be deduced from the observability of solutions localized in frequency according to a dyadic scale.
Externí odkaz:
http://arxiv.org/abs/2306.00536
The celebrated Rauch-Taylor/Bardos-Lebeau-Rauch geometric control condition is central in the study of the observability of the wave equation linking this property to high-frequency propagation along geodesics that are therays of geometric optics. Th
Externí odkaz:
http://arxiv.org/abs/2306.01023