Scattering in the Energy Space for Solutions of the Damped Nonlinear Schrödinger Equation on <inline-formula><math display="inline"><semantics><mrow><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mi>d</mi></msup><mo>×</mo><mi mathvariant="double-struck">T</mi></mrow></semantics></math></inline-formula>
We will show, in any space dimension <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mo>≥</mo><mn>3</mn></mrow></semantics></math></inlin...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-06-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/14/6/447 |
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| Summary: | We will show, in any space dimension <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>d</mi><mo>≥</mo><mn>3</mn></mrow></semantics></math></inline-formula>, the decay and scattering in the energy space for the solution to the damped nonlinear Schrödinger equation posed on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mi>d</mi></msup><mo>×</mo><mi mathvariant="double-struck">T</mi></mrow></semantics></math></inline-formula> and initial data in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>H</mi><mn>1</mn></msup><mrow><mo>(</mo><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mi>d</mi></msup><mo>×</mo><mi mathvariant="double-struck">T</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. We will also derive new bilinear Morawetz identities and corresponding localized Morawetz estimates. |
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| ISSN: | 2075-1680 |