Randomness and nonlinear evolution equations

DOI10.1007/s10114-019-8297-5zbMath1419.35255OpenAlexW2946512447WikidataQ127838680 ScholiaQ127838680MaRDI QIDQ2311723

Andrea R. Nahmod, Gigliola Staffilani

Publication date: 4 July 2019

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://hdl.handle.net/1721.1/125076

zbMATH Keywords

invarianceGibbs measureprobabilistic well-posedness

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Periodic solutions to PDEs (35B10) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs with randomness, stochastic partial differential equations (35R60) Free boundary problems for PDEs (35R35) Initial value problems for PDEs and systems of PDEs with constant coefficients (35E15)

Related Items (6)

Gibbs measures as unique KMS equilibrium states of nonlinear Hamiltonian PDEs ⋮ A microscopic derivation of Gibbs measures for the 1D focusing cubic nonlinear Schrödinger equation ⋮ The wave maps equation and Brownian paths ⋮ On the accept-reject mechanism for Metropolis-Hastings algorithms ⋮ Probabilistic small data global well-posedness of the energy-critical Maxwell-Klein-Gordon equation ⋮ Stochastic nonlinear Schrödinger equations in the defocusing mass and energy critical cases

Cites Work

• Unnamed Item
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• On the almost sure global well-posedness of energy sub-critical nonlinear wave equations on \(\mathbb R^{3}\)
• Almost sure well-posedness of the cubic nonlinear Schrödinger equation below \(L^{2}(\mathbb{T})\)
• The energy-critical defocusing NLS on \({\mathbb{T}}^{3}\)
• Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS
• Almost sure well-posedness for the periodic 3D quintic nonlinear Schrödinger equation below the energy space
• Random perturbation of PDEs and fluid dynamic models. École d'Été de Probabilités de Saint-Flour XL -- 2010
• Global well-posedness of the energy-critical nonlinear Schrödinger equation with small initial data in \(H^1(\mathbb T^3)\)
• Global Schrödinger maps in dimensions \(d\geq 2\): small data in the critical Sobolev spaces
• The Cauchy problem for quasi-linear Schrödinger equations
• Universality of the blow-up profile for small type II blow-up solutions of the energy-critical wave equation: the nonradial case
• Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation
• Anticipative Girsanov transformations
• Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrö\-dinger equation in the radial case
• Gevrey class regularity for the solutions of the Navier-Stokes equations
• Global flows with invariant (Gibbs) measures for Euler and Navier-Stokes two dimensional fluids
• Random data Cauchy theory for supercritical wave equations. II. A global existence result
• Random data Cauchy theory for supercritical wave equations I: Local theory
• On flows associated to Sobolev vector fields in Wiener spaces: An approach à la DiPerna-Lions
• KdV preserves white noise
• Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations
• The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices
• Nonlinear transformations on the Wiener space
• Nonlinear transformations of the canonical Gauss measure on Hilbert space and absolute continuity
• Periodic nonlinear Schrödinger equation and invariant measures
• Global flows with invariant measures for the inviscid modified SQG equations
• On nonlinear transformations of Gaussian measures
• On the ill-posedness of some canonical dispersive equations.
• Invariant measures for the 2D-defocusing nonlinear Schrödinger equation
• Profiles of bounded radial solutions of the focusing, energy-critical wave equation
• Two-dimensional nonlinear Schrödinger equation with random radial data
• A Pedestrian approach to the invariant Gibbs measures for the 2-\(d\) defocusing nonlinear Schrödinger equations
• Global existence and uniqueness of Schrödinger maps in dimensions \(d\geq 4\)
• Global well-posedness and scattering for the energy-critical Schrödinger equation in \(\mathbb R^{3}\)
• Absolute continuity of Brownian bridges under certain gauge transformations
• Universality of blow-up profile for small radial type II blow-up solutions of the energy-critical wave equation
• Local and global existence of smooth solutions for the stochastic Euler equations with multiplicative noise
• Long time dynamics for the one dimensional non linear Schrödinger equation
• Scattering below critical energy for the radial 4D Yang-Mills equation and for the 2D corotational wave map system
• Variable coefficient Schrödinger flows for ultrahyperbolic operators
• Transformations of Wiener integrals under translations
• On the probabilistic Cauchy theory of the cubic nonlinear Schrödinger equation on ℝ^{𝕕}, 𝕕≥3
• The Concentration-Compactness Rigidity Method for Critical Dispersive and Wave Equations
• Random Data Cauchy Theory for Nonlinear Wave Equations of Power-Type on ℝ³
• Gibbs measure for the periodic derivative nonlinear Schrödinger equation
• Low Regularity Local Well-Posedness of the Derivative Nonlinear Schrödinger Equation with Periodic Initial Data
• Scattering for 𝐻̇^{1/2} bounded solutions to the cubic, defocusing NLS in 3 dimensions
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• A bilinear estimate with applications to the KdV equation
• Quadratic forms for the 1-D semilinear Schrödinger equation
• Characterization of large energy solutions of the equivariant wave map problem: I
• Characterization of large energy solutions of the equivariant wave map problem: II
• Wiener randomization on unbounded domains and an application to almost sure well-posedness of NLS
• Almost Sure Existence of Global Weak Solutions for Supercritical Navier--Stokes Equations
• Stochastic differential equations. An introduction with applications.

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