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Record Nr. |
UNISA996503552103316 |
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Titolo |
Qualitative properties of dispersive PDEs / / Vladimir Georgiev, Alessandro Michelangeli, Raffaele Scandone, editors |
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Pubbl/distr/stampa |
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Singapore : , : Springer, , [2022] |
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©2022 |
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ISBN |
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Descrizione fisica |
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1 online resource (246 pages) |
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Collana |
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Springer INdAM series ; ; Volume 52 |
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Disciplina |
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Soggetti |
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Differential equations |
Functional analysis |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Intro -- Preface -- Organization -- Program Chairs -- Contents -- About the Editors -- Part I Long-Time Behavior of NLS-Type Equations -- A Note on Small Data Soliton Selection for Nonlinear Schrödinger Equations with Potential -- 1 Introduction -- 2 The Proof -- 2.1 Estimate of the Continuous Variable η -- 2.2 Estimate of Discrete Variables -- References -- Dynamics of Solutions to the Gross-Pitaevskii Equation Describing Dipolar Bose-Einstein Condensates -- 1 Introduction -- 1.1 Background -- 1.2 Main Results -- 1.2.1 Dynamics Below the Threshold -- 1.2.2 Dynamics Above the Threshold -- 1.2.3 Dynamics at the Threshold -- 2 Decay for Powers of Riesz Transforms and Virial Arguments -- 2.1 Integral Estimates for R4j -- 2.2 Point-Wise Estimates for R2j -- 2.3 Virial Identities -- 3 Sketch of the Proofs Below the Threshold -- 3.1 Scattering -- 3.2 Blow-up -- 3.3 Grow-up -- 4 Sketch of the Proofs Above the Threshold -- 5 Sketch of the Proofs at the Threshold -- References -- Part II Probabilistic and Nonstandard Methods in the Study of NLS Equations -- Almost Sure Pointwise Convergence of the Cubic Nonlinear Schrödinger Equation on T2 -- 1 Introduction -- 1.1 Notations and Terminology -- 2 Proof of Theorem 1 -- 2.1 Proof of Theorem 1 -- 3 Proof of Proposition 1 -- 3.1 Proof of Proposition 1 -- 4 Proof of Theorem 2 -- 4.1 Proof of Theorem 2 -- 4.2 Proof of Proposition 3 -- References -- Nonlinear Schrödinger Equation with Singularities -- 1 Introduction -- 2 The |
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