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  1. No Access

    Article

    The Wave Maps Equation and Brownian Paths

    We discuss the \((1+1)\) ( 1 + ...

    Bjoern Bringmann, Jonas Lührmann… in Communications in Mathematical Physics (2024)

  2. No Access

    Article

    Probabilistic Small Data Global Well-Posedness of the Energy-Critical Maxwell–Klein–Gordon Equation

    We establish probabilistic small data global well-posedness of the energy-critical Maxwell–Klein–Gordon equation relative to the Coulomb gauge for scaling super-critical random initial data. The proof relies o...

    Joachim Krieger, Jonas Lührmann… in Archive for Rational Mechanics and Analysis (2023)

  3. Article

    Open Access

    Global solutions of aggregation equations and other flows with random diffusion

    Aggregation equations, such as the parabolic-elliptic Patlak–Keller–Segel model, are known to have an optimal threshold for global existence versus finite-time blow-up. In particular, if the diffusion is absen...

    Matthew Rosenzweig, Gigliola Staffilani in Probability Theory and Related Fields (2023)

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  4. No Access

    Article

    2D-defocusing nonlinear Schrödinger equation with random data on irrational tori

    We revisit the work of Bourgain on the invariance of the Gibbs measure for the cubic, defocusing nonlinear Schrödinger equation in 2D on a square torus, and we prove the equivalent result on any tori.

    Chenjie Fan, Yumeng Ou, Gigliola Staffilani… in Stochastics and Partial Differential Equat… (2021)

  5. No Access

    Article

    Randomness and Nonlinear Evolution Equations

    In this paper we survey some results on existence, and when possible also uniqueness, of solutions to certain evolution equations obtained by injecting randomness either on the set of initial data or as a pert...

    Andrea R. Nahmod, Gigliola Staffilani in Acta Mathematica Sinica, English Series (2019)

  6. No Access

    Article

    Global flows with invariant measures for the inviscid modified SQG equations

    We consider the family known as modified or generalized surface quasi-geostrophic equations (mSQG) consisting of the classical inviscid surface quasi-geostrophic (SQG) equation together with a family of regula...

    Andrea R. Nahmod, Nataša Pavlović… in Stochastics and Partial Differential Equa… (2018)

  7. No Access

    Article

    Randomization and the Gross–Pitaevskii Hierarchy

    We study the Gross–Pitaevskii hierarchy on the spatial domain \({\mathbb{T}^3}\) ...

    Vedran Sohinger, Gigliola Staffilani in Archive for Rational Mechanics and Analysis (2015)

  8. No Access

    Article

    On the Continuum Limit for Discrete NLS with Long-Range Lattice Interactions

    We consider a general class of discrete nonlinear Schrödinger equations (DNLS) on the lattice \({h\mathbb{Z}}\) with ...

    Kay Kirkpatrick, Enno Lenzmann… in Communications in Mathematical Physics (2013)

  9. No Access

    Article

    Semilinear Schrödinger flows on hyperbolic spaces: scattering in H 1

    We prove global well-posedness and scattering in H 1 for the defocusing nonlinear Schrödinger equations $$\left\{\begi...

    Alexandru D. Ionescu, Gigliola Staffilani in Mathematische Annalen (2009)

  10. No Access

    Article

    Scattering Theory for Radial Nonlinear Schrödinger Equations on Hyperbolic Space

    We study the long-time behavior of radial solutions to nonlinear Schrödinger equations on hyperbolic space. We show that the usual distinction between short-range and long-range nonlinearity is modified: the g...

    Valeria Banica, Rémi Carles, Gigliola Staffilani in Geometric and Functional Analysis (2008)

  11. Article

    Errata to “Low Regularity Solutions for the Kadomtsev–Petviashvili I Equation”, GAFA, Geom. Funct. Anal. 13 (2003), 737-794

    James Colliander, Carlos E. Kenig… in GAFA Geometric And Functional Analysis (2007)

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  12. No Access

    Article

    Symplectic nonsqueezing of the korteweg-de vries flow

    James Colliander, Gigliola Staffilani, Markus Keel, Hideo Takaoka… in Acta Mathematica (2005)

  13. No Access

    Article

    Local well-posedness for higher order nonlinear dispersive systems

    We study nonlinear dispersive systems of the form $$\partial _t u_k + \partial _x^{(2j + 1)} uk + P_k (u_l , \ldots u_n , \ldots ,\pa...

    Carlos E. Kenig, Gigliola Staffilani in Journal of Fourier Analysis and Applications (1997)