Zobrazeno 1 - 10
of 1 106
pro vyhledávání: '"Tzvetkov, P."'
We introduce modified energies that are suitable to get upper bounds on the high Sobolev norms for solutions to the $1$D periodic NLS. Our strategy is rather flexible and allows us to get a new and simpler proof of the bounds obtained by Bourgain in
Externí odkaz:
http://arxiv.org/abs/2407.17993
We extend Bourgain's $L^2$-wellposedness result for the KP-II equation on $\mathbb{T}^2$ to initial data with negative Sobolev regularity. The key ingredient is a new linear $L^4$-Strichartz estimate which is effective on frequency-dependent time sca
Externí odkaz:
http://arxiv.org/abs/2407.12222
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:
Alphonse, Paul, Tzvetkov, Nikolay
We show that, after a renormalisation, one can define the square of the modulus of the solution of the fractional Schr\"odinger equations on the circle with data in Sobolev spaces of arbitrary negative index. As an application, we obtain observabilit
Externí odkaz:
http://arxiv.org/abs/2403.12763
We study the fractional $\Phi^4_3$-measure (with order $\alpha > 1$) and the dynamical problem of its canonical stochastic quantization: the three-dimensional stochastic damped fractional nonlinear wave equation with a cubic nonlinearity, also called
Externí odkaz:
http://arxiv.org/abs/2311.00543
In the study of partial differential equations (PDEs) with random initial data and singular stochastic PDEs with random forcing, we typically decompose a classically ill-defined solution map into two steps, where, in the first step, we use stochastic
Externí odkaz:
http://arxiv.org/abs/2309.16504
Publikováno v:
Scientific Reports, Vol 14, Iss 1, Pp 1-8 (2024)
Abstract We analyzed data from positively tested COVID-19 outpatients to describe self-medication with OTC drugs and use of other remedies against symptoms of SARS-CoV-2 infection. We specifically considered their type and frequency, as well as assoc
Externí odkaz:
https://doaj.org/article/830b1efe90234eaab8df62d5e4dc9413
Quasi-invariance of Gaussian measures for the $3d$ energy critical nonlinear Schr\' odinger equation
Autor:
Sun, Chenmin, Tzvetkov, Nikolay
We consider the $3d$ energy critical nonlinear Schr\" odinger equation with data distributed according to the Gaussian measure with covariance operator $(1-\Delta)^{-s}$, where $\Delta$ is the Laplace operator and $s$ is sufficiently large. We prove
Externí odkaz:
http://arxiv.org/abs/2308.12758