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arXiv · 2110.13717

Existence and stability of stationary solutions to the compressible quantum model

Xiaoyu Xi
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Abstract

In this paper, the compressible quantum model with the given mass source and the external force of general form in three-dimensional whole space is considered. Based on the weighted $L^2$ method and $L^\infty$ estimates, the existence and uniqueness of stationary solutions can be obtained by the contraction mapping principle. By using a general energy method, the nonlinear stability of stationary solutions is studied, and the time decay rates of the solutions are established when the initial perturbation belongs to $\dot{H}^{-s}$ with $0 \leq s < \frac{3}{2}$.

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Xiaoyu Xi. 2021-10-26. Existence and stability of stationary solutions to the compressible quantum model. https://arxiv.org/abs/2110.13717

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