Zobrazeno 1 - 10
of 83
pro vyhledávání: '"Haus, Emanuele"'
We consider the Kirchhoff equation on tori of any dimension and we construct solutions whose Sobolev norms oscillates in a chaotic way on certain long time scales. The chaoticity is encoded in the time between oscillations of the norm, which can be c
Externí odkaz:
http://arxiv.org/abs/2303.00688
Motivated by the problem of long time stability vs. instability of KAM tori of the Nonlinear cubic Schr\"odinger equation (NLS) on the two dimensional torus $\mathbb T^2:= (\mathbb R/2\pi \mathbb Z)^2$, we consider a quasi-periodically forced NLS equ
Externí odkaz:
http://arxiv.org/abs/2208.02040
Autor:
Baldi, Pietro, Haus, Emanuele
We consider the Kirchhoff equation $$ \partial_{tt} u - \Delta u \Big( 1 + \int_{\mathbb T^d} |\nabla u|^2 \Big) = 0 $$ on the $d$-dimensional torus $\mathbb T^d$, and its Cauchy problem with initial data $u(0,x)$, $\partial_t u(0,x)$ of size $\varep
Externí odkaz:
http://arxiv.org/abs/2007.03543
Autor:
Baldi, Pietro, Haus, Emanuele
Consider the Kirchhoff equation $$ \partial_{tt} u - \Delta u \Big( 1 + \int_{\mathbb{T}^d} |\nabla u|^2 \Big) = 0 $$ on the $d$-dimensional torus $\mathbb{T}^d$. In a previous paper we proved that, after a first step of quasilinear normal form, the
Externí odkaz:
http://arxiv.org/abs/2006.01136
Autor:
Baldi, Pietro, Haus, Emanuele
We investigate a general question about the size and regularity of the data and the solutions in implicit function problems with loss of regularity. First, we give a heuristic explanation of the fact that the optimal data size found by Ekeland and S\
Externí odkaz:
http://arxiv.org/abs/1906.12290
Autor:
Haus, Emanuele, Maspero, Alberto
We consider the semiclassical Schr\"odinger equation on $\mathbb R^d$ given by $$\mathrm{i} \hbar \partial_t \psi = \left(-\frac{\hbar^2}{2} \Delta + W_l(x) \right)\psi + V(t,x)\psi ,$$ where $W_l$ is an anharmonic trapping of the form $W_l(x)= \frac
Externí odkaz:
http://arxiv.org/abs/1904.03703
We rigorously show the existence of a rotationally and centrally symmetric "lens-shaped" cluster of three surfaces, meeting at a smooth common circle, forming equal angles of 120 degrees, self-shrinking under the motion by mean curvature.
Commen
Commen
Externí odkaz:
http://arxiv.org/abs/1811.07822
We consider the defocusing cubic nonlinear Schr\"odinger equation (NLS) on the two-dimensional torus. The equation admits a special family of elliptic invariant quasiperiodic tori called finite-gap solutions. These are inherited from the integrable 1
Externí odkaz:
http://arxiv.org/abs/1810.03694
Autor:
Baldi, Pietro, Haus, Emanuele
We consider the Cauchy problem for the Kirchhoff equation on $\mathbb{T}^d$ with initial data of small amplitude $\varepsilon$ in Sobolev class. We prove a lower bound $\varepsilon^{-4}$ for the existence time, which improves the bound $\varepsilon^{
Externí odkaz:
http://arxiv.org/abs/1805.01189