☆ 4.7 Article

Refined probabilistic local well-posedness for a cubic Schrödinger half-wave equation

JOURNAL OF DIFFERENTIAL EQUATIONS (2024)

Related references

Note: Only part of the references are listed.

Article Mathematics

Unbounded Hankel operators and the flow of the cubic Szego equation

Patrick Gerard et al.

Summary: In this paper, we prove that for any Hankel operator with a symbol from the Hardy class H-2, the maximal and minimal domains coincide. As an application, we demonstrate that the evolution flow of the cubic Szegő equation on the unit circle can be continuously extended to the whole class H-2.

INVENTIONES MATHEMATICAE (2023)

Add to Collection

Article Mathematics

Pathological Set of Initial Data for Scaling-Supercritical Nonlinear Schrodinger Equations

Nicolas Camps et al.

Summary: The aim of this work is to prove the existence of pathological initial data, for which the regularized solutions by convolution experience a norm-inflation mechanism in very short time. This result follows the construction approach of Sun and Tzvetkov, where the pathological set consists of a superposition of profiles that concentrate at different points. Due to the finite propagation speed of the wave equation, only one profile can exhibit significant growth within a given time. However, for Schrodinger-type equations, the interaction between profiles cannot be excluded. Instead, a method is proposed to exploit the regularizing effect of the approximate identity, which prevents the norm inflation of profiles concentrated at smaller scales.

INTERNATIONAL MATHEMATICS RESEARCH NOTICES (2023)

Add to Collection

Article Mathematics

Global well-posedness for the derivative nonlinear Schrodinger equation

Hajer Bahouri et al.

Summary: This paper studies the derivative nonlinear Schrodinger equation on the real line, proving global well-posedness for general Cauchy data in H-1/2(R) and showing that the H-1/2 norm of the solutions remains globally bounded in time. The proof is achieved by combining profile decomposition techniques with the integrability structure of the equation.

INVENTIONES MATHEMATICAE (2022)

Add to Collection

Article Mathematics

Probabilistic local well-posedness for the Schrodinger equation posed for the Grushin Laplacian

Louise Gassot et al.

Summary: In this article, we study the local well-posedness of the nonlinear Schrodinger equation associated to the Grushin operator with random initial data. We prove that there exists a large family of initial data such that, with respect to a suitable randomization in H-k, k is an element of (1, 3/2], almost-sure local well-posedness holds. The proof relies on bilinear and trilinear estimates.

JOURNAL OF FUNCTIONAL ANALYSIS (2022)

Add to Collection

Article Mathematics

Almost Sure Local Well-Posedness for a Derivative Nonlinear Wave Equation

Bjoern Bringmann

Summary: The study focuses on the local existence of solutions for a one-dimensional nonlinear wave equation at super-critical regularities, overcoming the challenge of the absence of nonlinear smoothing effect through an adaptive iterative decomposition method.

INTERNATIONAL MATHEMATICS RESEARCH NOTICES (2021)

Add to Collection

Article Mathematics, Applied

Remarks on solitary waves and Cauchy problem for Half-wave-Schrodinger equations

Yakine Bahri et al.

Summary: This paper focuses on solitary wave solutions of the Cauchy problem for the Half-wave Schrodinger equation in the plane, demonstrating the existence and orbital stability of ground states, proving the existence of traveling wave solutions for any speed v that converge to zero wave as velocity tends to 1, and solving the Cauchy problem for initial data with s > 1/2 in (LxHys)-H-2(R-2). The critical case of s = 1/2 remains an interesting open problem.

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS (2021)

Add to Collection

Article Mathematics, Applied

Transverse Stability of Line Soliton and Characterization of Ground State for Wave Guide Schrodinger Equations

Yakine Bahri et al.

Summary: This paper investigates the transverse stability of line Schrodinger soliton under a full wave guide Schrodinger flow on a cylindrical domain, and characterizes the ground state of the wave guide Schrodinger equation. The critical frequency and properties of the ground states are established for different ranges of frequency.

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS (2021)

Add to Collection

Article Mathematics, Applied

Refined probabilistic global well-posedness for the weakly dispersive NLS

Chenmin Sun et al.

Summary: The study focuses on cubic fractional NLS with weak dispersion and data distributed according to the Gibbs measure. By constructing root natural strong solutions, the research improves upon previous results and relies on new ideas to overcome difficulties caused by weakly dispersive effect.

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS (2021)

Add to Collection

Article Physics, Mathematical

Invariant Gibbs measure and global strong solutions for the Hartree NLS equation in dimension three

Yu Deng et al.

Summary: This paper investigates the defocusing Hartree nonlinear Schrodinger equations on T3 with specific properties, demonstrating the invariance of the associated Gibbs measure and global existence of strong solutions by using the method of random averaging operators. These findings extend previous research and relax the related requirements.

JOURNAL OF MATHEMATICAL PHYSICS (2021)

Add to Collection

Article Mathematics

AN OPTIMAL REGULARITY RESULT ON THE QUASI-INVARIANT GAUSSIAN MEASURES FOR THE CUBIC FOURTH ORDER NONLINEAR SCHRODINGER EQUATION

Tadahiro Oh et al.

JOURNAL DE L ECOLE POLYTECHNIQUE-MATHEMATIQUES (2018)

Add to Collection

Article Mathematics

Unbounded Sobolev trajectories and modified scattering theory for a wave guide nonlinear Schrodinger equation

Haiyan Xu

MATHEMATISCHE ZEITSCHRIFT (2017)

Add to Collection

Article Mathematics

The cubic Szegő equation

Patrick Gérard et al.

ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE (2017)

Add to Collection

Article Mathematics, Applied

MODIFIED SCATTERING FOR THE CUBIC SCHRODINGER EQUATION ON PRODUCT SPACES AND APPLICATIONS

Zaher Hani et al.

FORUM OF MATHEMATICS PI (2015)

Add to Collection

Article Mathematics

Uniqueness of non-linear ground states for fractional Laplacians in

Rupert L. Frank et al.

ACTA MATHEMATICA (2013)

Add to Collection

Article Mathematics

Invariant tori for the cubic Szego equation

Patrick Gerard et al.

INVENTIONES MATHEMATICAE (2012)

Add to Collection

Article Mathematics, Applied

EFFECTIVE INTEGRABLE DYNAMICS FOR A CERTAIN NONLINEAR WAVE EQUATION

Patrick Gerard et al.

ANALYSIS & PDE (2012)

Add to Collection

Article Mathematics, Applied

Remarks on Nonlinear Smoothing under Randomization for the Periodic KdV and the Cubic Szego Equation

Tadahiro Oh

FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA (2011)

Add to Collection

Article Mathematics, Applied

ON THE WAVE EQUATION WITH QUADRATIC NONLINEARITIES IN THREE SPACE DIMENSIONS

Axel Gruenrock

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS (2011)

Add to Collection

Article Mathematics, Applied

TRAVELING WAVES FOR THE CUBIC SZEGO EQUATION ON THE REAL LINE

Oana Pocovnicu

ANALYSIS & PDE (2011)

Add to Collection

Article Mathematics, Applied

Well-posedness and scattering for the KP-II equation in a critical space

Martin Hadac et al.

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE (2009)

Add to Collection

Article Mathematics

Random data Cauchy theory for supercritical wave equations II: a global existence result

Nicolas Burq et al.

INVENTIONES MATHEMATICAE (2008)

Add to Collection

Article Mathematics

Random data Cauchy theory for supercritical wave equations I: local theory

Nicolas Burq et al.

INVENTIONES MATHEMATICAE (2008)

Add to Collection

Article Mathematics

Multilinear eigenfunction estimates and global existence for the three dimensional nonlinear Schrodinger equations

N Burq et al.

ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE (2005)

Add to Collection

Article Mathematics

Bilinear eigenfunction estimates and the nonlinear Schrodinger equation on surfaces

N Burq et al.

INVENTIONES MATHEMATICAE (2005)

Add to Collection

Article Mathematics

Ill-posedness for the derivative Schrodinger and generalized Benjamin-Ono equations

HA Biagioni et al.

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY (2001)

Add to Collection

© Peeref 2019-2024. All rights reserved.