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Global axisymmetric solutions to the 3D Navier--Stokes--Poisson--Nernst--Planck system in the exterior of a cylinder

Jihong Zhao
대한수학회 (The Korean Mathematical Society)|2021.05|대한수학회보 (Bulletin of the KMS)|제58권 제3호|pp. 729-744|DOI 10.4134/BKMS.b200536

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global existenceNavier--Stokes--Poisson--Nernst--Planck equationsaxisymmetric solutions
주제분류수학

초록

In this paper we prove global existence and uniqueness of axisymmetric strong solutions for the three dimensional electro-hydrodyna\-mic model based on the coupled Navier--Stokes--Poisson--Nernst--Planck system in the exterior of a cylinder. The key ingredient is that we use the axisymmetry of functions to derive the $L^{p}$ interpolation inequalities, which allows us to establish all kinds of a priori estimates for the velocity field and charged particles via several cancellation laws.

Abstract

In this paper we prove global existence and uniqueness of axisymmetric strong solutions for the three dimensional electro-hydrodyna\-mic model based on the coupled Navier--Stokes--Poisson--Nernst--Planck system in the exterior of a cylinder. The key ingredient is that we use the axisymmetry of functions to derive the $L^{p}$ interpolation inequalities, which allows us to establish all kinds of a priori estimates for the velocity field and charged particles via several cancellation laws.

참고문헌 (20)

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