具有随机初值的 Navier-Stokes Nernst-Planck-Poisson 方程在超临界 Sobolev 空间的适定性
The Well-Posedness for the Navier-Stokes Nernst-Planck-Poisson Equations with Random Initial Data in SupercriticalSobolev Space
DOI: 10.12677/AAM.2025.1412523, PDF,    国家自然科学基金支持
作者: 祝振凯, 郑云涵, 杜利怀：温州大学数理学院，浙江 温州；耿金波*：浙江师范大学数学科学学院，浙江 金华
关键词: 随机初值；超临界 Sobolev 空间；Navier-Stokes Nernst-Planck-Poisson 方程；Random Initial Data； Supercritical Sobolev Space； Navier-Stokes Nernst-Planck-Poisson Equations
摘要: 本文考虑 d 维全空间上 Navier-Stokes Nernst-Planck-Poisson 方程的适定性问题。经过适当 的随机化后，我们获得了初值在超临界 Sobolev 空间中解的局部存在性和唯一性。此外，还建立 了全局解存在的概率估计。
Abstract: In this paper, we consider the problem of the Navier-Stokes Nernst-Planck-Poisson Equations on d-dimensional full space. After a suitable randomization, we obtain the local existence anduniqueness of the solution with the initial data in supercriti- cal Sobolev space. Furthermore, the probability estimate of global existence is also established.
文章引用：祝振凯, 郑云涵, 杜利怀, 耿金波. 具有随机初值的 Navier-Stokes Nernst-Planck-Poisson 方程在超临界 Sobolev 空间的适定性[J]. 应用数学进展, 2025, 14(12): 484-503. https://doi.org/10.12677/AAM.2025.1412523

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