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pro vyhledávání: '"Nahmod, Andrea"'
In this proceedings article we survey the results in [5] and their motivation, as presented at the 50th Journ\'ees EDP 2024. With the aim of quantifying turbulent behaviors of vortex filaments, we study the multifractality of a family of generalized
Externí odkaz:
http://arxiv.org/abs/2412.04926
With the aim of quantifying turbulent behaviors of vortex filaments, we study the multifractality and intermittency of the family of generalized Riemann's non-differentiable functions \begin{equation} R_{x_0}(t) = \sum_{n \neq 0} \frac{e^{2\pi i ( n^
Externí odkaz:
http://arxiv.org/abs/2309.08114
Autor:
Agrawal, Siddhant, Nahmod, Andrea R.
We consider the 2D incompressible Euler equation on a bounded simply connected domain $\Omega$. We give sufficient conditions on the domain $\Omega$ so that for all initial vorticity $\omega_0 \in L^{\infty}(\Omega)$ the weak solutions are unique. Ou
Externí odkaz:
http://arxiv.org/abs/2308.12926
In this note we further discuss the probabilistic scaling introduced by the authors in [21, 22]. In particular we do a case study comparing the stochastic heat equation, the nonlinear wave equation and the nonlinear Schrodinger equation.
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Externí odkaz:
http://arxiv.org/abs/2308.08411
Autor:
Miller, Joseph K., Nahmod, Andrea R., Pavlović, Nataša, Rosenzweig, Matthew, Staffilani, Gigliola
We consider the Vlasov equation in any spatial dimension, which has long been known to be an infinite-dimensional Hamiltonian system whose bracket structure is of Lie-Poisson type. In parallel, it is classical that the Vlasov equation is a mean-field
Externí odkaz:
http://arxiv.org/abs/2206.07589
We prove the invariance of the Gibbs measure under the dynamics of the three-dimensional cubic wave equation, which is also known as the hyperbolic $\Phi^4_3$-model. This result is the hyperbolic counterpart to seminal works on the parabolic $\Phi^4_
Externí odkaz:
http://arxiv.org/abs/2205.03893
In this paper we consider the defocusing Hartree nonlinear Schr\"odinger equations on $\mathbb T^3$ with real valued and even potential $V$ and Fourier multiplier decaying like $|k|^{-\beta}$. By relying on the method of random averaging operators in
Externí odkaz:
http://arxiv.org/abs/2101.11100
Uniqueness of the 2D Euler equation on a corner domain with non-constant vorticity around the corner
Autor:
Agrawal, Siddhant, Nahmod, Andrea R.
We consider the 2D incompressible Euler equation on a corner domain $\Omega$ with angle $\nu\pi$ with $\frac{1}{2}<\nu<1$. We prove that if the initial vorticity $\omega_0 \in L^{1}(\Omega)\cap L^{\infty}(\Omega)$ and if $\omega_0$ is non-negative an
Externí odkaz:
http://arxiv.org/abs/2009.14816
Abstract. The purpose of this paper is twofold. We introduce the theory of random tensors, which naturally extends the method of random averaging operators in our earlier work arXiv:1910.08492, to study the propagation of randomness under nonlinear d
Externí odkaz:
http://arxiv.org/abs/2006.09285
We consider the defocusing nonlinear Schr\"odinger equation on $\mathbb{T}^2$ with Wick ordered power nonlinearity, and prove almost sure global well-posedness with respect to the associated Gibbs measure. The heart of the matter is the uniqueness of
Externí odkaz:
http://arxiv.org/abs/1910.08492