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Quasi-invariance of low regularity Gaussian measures under the gauge map of the periodic derivative NLS
Genovese, G.; Lucà, R.
; Tzvetkov, N. (2022-01-01)
; Tzvetkov, N. (2022-01-01)
The periodic DNLS gauge is an anticipative map with singular generator which revealed crucial in the study of the periodic derivative NLS. We prove quasi-invariance of the Gaussian measure on L2(T) with covariance [1+(−Δ)s]−1 ...
The Frisch–Parisi formalism for fluctuations of the Schrödinger equation
Kumar, S.; Ponce Vanegas, F.; Roncal, L.; Vega, L. (2022)
; Roncal, L.; Vega, L. (2022)
We consider the solution of the Schrödinger equation $u$ in $\mathbb{R}$ when the initial datum tends to the Dirac comb. Let $h_{\text{p}, \delta}(t)$ be the fluctuations in time of $\int\lvert x \rvert^{2\delta}\lvert ...
On the Schrödinger map for regular helical polygons in the hyperbolic space
(2022-01-01)
The main purpose of this article is to understand the evolution of X t = X s ∧− X ss , with X(s, 0) a regular polygonal curve with a nonzero torsion in the three-dimensional Minkowski space. Unlike in the case of the ...
ENERGY CONSERVATION FOR 2D EULER WITH VORTICITY IN L(log L)α*
(2022-01-01)
In these notes we discuss the conservation of the energy for weak solutions of the twodimensional incompressible Euler equations. Weak solutions with vorticity in (Formula presented) with p > 3/2 are always conservative, ...