Cauchy Problem for Stochastic Nonlinear Schrödinger Equation with Nonlinear Energy-Critical Damping
We consider the Cauchy problem for the stochastic nonlinear Schrödinger equation augmented by nonlinear energy-critical damping term arising in nonlinear optics and quantum field theory. Through examining the behavior of the momentum and energy functionals, we almost surely prove the existence and u...
| Published in: | Mathematics |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-08-01
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| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/12/16/2501 |
| Summary: | We consider the Cauchy problem for the stochastic nonlinear Schrödinger equation augmented by nonlinear energy-critical damping term arising in nonlinear optics and quantum field theory. Through examining the behavior of the momentum and energy functionals, we almost surely prove the existence and uniqueness of global solutions with continuous <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><mi mathvariant="double-struck">R</mi><mi>d</mi></msup><mo>)</mo></mrow></mrow></semantics></math></inline-formula> valued paths. The results cover either defocusing nonlinearity in the full energy critical and subcritical range of exponents or focusing nonlinearity in the full subcritical range, as in the deterministic case. |
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| ISSN: | 2227-7390 |