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arXiv · 2004.08952

Multilinear Weighted Estimates and Quantum Zakharov System

Brian J Choi
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Abstract

We consider the compact case of one-dimensional quantum Zakharov system, as an initial-value problem with periodic boundary conditions. We apply the Bourgain norm method to show low regularity local well-posedness for a certain class of Sobolev exponents that are sharp up to the boundary, under the condition that Schr\"odinger Sobolev regularity is non-negative. Using the conservation law and energy method, we show global well-posedness for sufficiently regular initial data, without any smallness assumption. Lastly we show the semi-classical limit as $\epsilon \to 0$ on a compact time interval, whereas the quantum perturbation proves to be singular on an infinite time interval.

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Brian J Choi. 2020-04-19. Multilinear Weighted Estimates and Quantum Zakharov System. https://doi.org/10.3846/mma.2022.15555

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