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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.
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참고문헌 (20)
참고문헌 신청
K. Abe / 2020 / Axisymmetric flows in the exterior of a cylinder / Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150(4):1671~1698
Hammadi Abidi / 2008 / Résultats de régularité de solutions axisymétriques pour le système de Navier–Stokes / Bulletin des Sciences Mathématiques 132(7):592~624
Jishan Fan / 2013 / Regularity criteria for a mathematical model for the deformation of electrolyte droplets / Applied Mathematics Letters 26(4):494~499
Jishan Fan / 2012 / On the Cauchy problem for a model of electro-kinetic fluid / Applied Mathematics Letters 25(1):33~37
Eberhard Hopf / 1950 / Uber die Anfangswertaufgabe f¨ur die hydrodynamischen Grundgleichungen ¨ / Math. Nachr 4(1-6):213~231
Hammadi Abidi / 2008 / Résultats de régularité de solutions axisymétriques pour le système de Navier–Stokes / Bulletin des Sciences Mathématiques 132(7):592~624
Jishan Fan / 2013 / Regularity criteria for a mathematical model for the deformation of electrolyte droplets / Applied Mathematics Letters 26(4):494~499
Jishan Fan / 2012 / On the Cauchy problem for a model of electro-kinetic fluid / Applied Mathematics Letters 25(1):33~37
Eberhard Hopf / 1950 / Uber die Anfangswertaufgabe f¨ur die hydrodynamischen Grundgleichungen ¨ / Math. Nachr 4(1-6):213~231
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