• ALMOST SURE POINTWISE CONVERGENCE OF THE CUBIC NONLINEAR SCHRODINGER EQUATION ON ̈ T 2 

  Lucà, R. (2022)

  We revisit a result from “Pointwise convergence of the Schr ̈odinger flow, E. Compaan, R. Luc`a, G. Staffilani, International Mathematics Research Notices, 2021 (1), 596-647” regarding the pointwise convergence of ...

• Lifespan estimates for the compressible Euler equations with damping via Orlicz spaces techniques 

  Lai, N-A; Schiavone, N.M. (2023-10-06)

  In this paper we are interested in the upper bound of the lifespan estimate for the compressible Euler system with time dependent damping and small initial perturbations. We employ some techniques from the blow-up study ...

• Eigenvalue Curves for Generalized MIT Bag Models 

  Arrizabalaga, N.; Mas, A.; Sanz-Perela, T.; Vega, L. (2021)

  We study spectral properties of Dirac operators on bounded domains Ω ⊂ R 3 with boundary conditions of electrostatic and Lorentz scalar type and which depend on a parameter τ ∈ R; the case τ = 0 corresponds to the MIT ...

• On the existence of weak solutions for the 2D incompressible Euler equations with in-out flow and source and sink points 

  Bravin, M. (2021)

  Well-posedness for the two dimensional Euler system with given initial vorticity is known since the works of Judoviˇc. In this paper we show existence of solutions in the case where we allowed the fluid to enter in and ...

• Unbounded growth of the energy density associated to the Schrödinger map and the binormal flow 

  Banica, V.; Vega, L. (2021)

  We consider the binormal flow equation, which is a model for the dynamics of vortex filaments in Euler equations. Geometrically it is a flow of curves in three dimensions, explicitly connected to the 1-D Schr¨odinger map ...

• On the one dimensional cubic NLS in a critical space 

  Bravin, M.; Vega, L. (2021)

  In this note we study the initial value problem in a critical space for the one dimensional Schr¨odinger equation with a cubic non-linearity and under some smallness conditions. In particular the initial data is given by ...

• On the Calderón problem for nonlocal Schrödinger equations with homogeneous, directionally antilocal principal symbols 

  Covi, G.; García-Ferrero, M.A.; Rüland, A. (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 ...

• Sharp local smoothing estimates for Fourier integral operators 

  Beltran D.; Hickman J.; Sogge C.D. (2019)

  The theory of Fourier integral operators is surveyed, with an emphasis on local smoothing estimates and their applications. After reviewing the classical background, we describe some recent work of the authors which ...

• ENERGY CONSERVATION FOR 2D EULER WITH VORTICITY IN L(log L)α* 

  Ciampa, G. (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, ...

• On the Hausdorff dimension of Riemann's non-differentiable function 

  Eceizabarrena, D. (2021-01-01)

  Recent findings show that the classical Riemann's non-differentiable function has a physical and geometric nature as the irregular trajectory of a polygonal vortex filament driven by the binormal flow. In this article, we ...

• A pseudospectral method for the one-dimensional fractional Laplacian on R 

  Cayama, J.; Cuesta, C.M.; De la Hoz, F. (2021-01-15)

  In this paper, we propose a novel pseudospectral method to approximate accurately and efficiently the fractional Laplacian without using truncation. More precisely, given a bounded regular function defined over R, we map ...

• Discrepancy of Minimal Riesz Energy Points 

  Marzo, J.; Mas, A. (2021-12-01)

  We find upper bounds for the spherical cap discrepancy of the set of minimizers of the Riesz s-energy on the sphere Sd. Our results are based on bounds for a Sobolev discrepancy introduced by Thomas Wolff in an unpublished ...

• Self-adjointness of two-dimensional Dirac operators on corner domains 

  Pizzichillo, F.; Van Den Bosch, H. (2021-01-01)

  We investigate the self-adjointness of the two-dimensional Dirac operator D, with quantum-dot and Lorentz-scalar i-shell boundary conditions, on piecewise C2 domains (with finitely many corners). For both models, we prove ...

• Dirac Operators and Shell Interactions: A Survey 

  Ourmières-Bonafos, T.; Pizzichillo, F. (2021-01-01)

  In this survey we gather recent results on Dirac operators coupled with δ-shell interactions. We start by discussing recent advances regarding the question of self-adjointness for these operators. Afterwards we switch to ...

• On the regularity of solutions to the k-generalized korteweg-de vries equation 

  Kenig, C. E.; Linares, F.; Ponce, G.; Vega, L. (2018-01-01)

  This work is concerned with special regularity properties of solutions to the k-generalized Korteweg-de Vries equation. In [Comm. Partial Differential Equations 40 (2015), 1336–1364] it was established that if the initial ...

• The Frisch–Parisi formalism for fluctuations of the Schrödinger equation 

  Kumar, S.; Ponce Vanegas, F.; 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 

  Kumar, S. (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 ...

• Pointwise Convergence of the Schr\"odinger Flow 

  Compaan, E.; Lucà, R.; Staffilani, G. (2021-01)

  In this paper we address the question of the pointwise almost everywhere limit of nonlinear Schr\"odinger flows to the initial data, in both the continuous and the periodic settings. Then we show how, in some cases, certain ...

• 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)

  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 ...

• Numerical approximation of the fractional Laplacian on R using orthogonal families 

  Cayama, J.; Cuesta, C.M.; De la Hoz, F. (2020-12-01)

  In this paper, using well-known complex variable techniques, we compute explicitly, in terms of the F12 Gaussian hypergeometric function, the one-dimensional fractional Laplacian of the complex Higgins functions, the complex ...

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