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On the theory of weak turbulence for the nonlinear Schrodinger equation / M. Escobedo and J.J.L. Velazquez.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v 238, no 1124.Publication details: Providence : American Mathematical Society, 2015.Description: v, 107 p. : 26 cmISBN:
  • 9781470414344 (alk. paper)
Subject(s): DDC classification:
  • 510 23 Am512
Contents:
1. Introduction -- 2. Well-posedness results -- 3. Qualitative behaviors of the solutions -- 4. Solutions without condensation: pulsating behavior -- 5. Heuristic arguments and open problems -- 6. Auxiliary results -- Bibliography -- Index.
Summary: The authors study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrodinger equation. They define suitable concepts of weak and mild solutions and prove local and global well posedness results. Several qualitative properties of the solutions, including long time asymptotics, blow up results and condensation in finite time are obtained. The authors also prove the existence of a family of solutions that exhibit pulsating behavior.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 510 Am512 (Browse shelf(Opens below)) Available 136726
Total holds: 0

Includes bibliographical references and index.

1. Introduction --
2. Well-posedness results --
3. Qualitative behaviors of the solutions --
4. Solutions without condensation: pulsating behavior --
5. Heuristic arguments and open problems --
6. Auxiliary results --
Bibliography --
Index.

The authors study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrodinger equation. They define suitable concepts of weak and mild solutions and prove local and global well posedness results. Several qualitative properties of the solutions, including long time asymptotics, blow up results and condensation in finite time are obtained. The authors also prove the existence of a family of solutions that exhibit pulsating behavior.

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