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On the Calderón problem for nonlocal Schrödinger equations with homogeneous, directionally antilocal principal symbols
(2022-12-25)
In this article we consider direct and inverse problems for α-stable, elliptic nonlocal operators whose kernels are possibly only supported on cones and which satisfy the structural condition of directional antilocality ...
The Frisch–Parisi formalism for fluctuations of the Schrödinger equation
(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 ...
Quasi-invariance of low regularity Gaussian measures under the gauge map of the periodic derivative NLS
(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 ...
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, ...