Almost Periodic Solutions of Navier–Stokes–Ohm Type Equations in Magneto-Hydrodynamics

Evagelia S. Athanasiadou (), Vasileios F. Dionysatos (), Panagiotis N. Koumantos () and Panaiotis K. Pavlakos ()
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Evagelia S. Athanasiadou: National and Kapodistrian University of Athens
Vasileios F. Dionysatos: National and Kapodistrian University of Athens
Panagiotis N. Koumantos: National and Kapodistrian University of Athens
Panaiotis K. Pavlakos: National and Kapodistrian University of Athens

A chapter in Applications of Mathematics and Informatics in Science and Engineering, 2014, pp 43-57 from Springer

Abstract: Abstract In this paper we construct (Bohl-Bohr- and Stepanoff-) almost periodic solutions of an evolution equation of the form d d t + A x ( t ) = F ( t , x ( t ) ) $$\left ( \frac{d} {dt} + A\right )x(t) = F(t,x(t))$$ , t ∈ ℝ $$t \in \mathbb{R}$$ , describing the velocity and the magnetic field of a viscous incompressible homogeneous ideal plasma in magneto-hydrodynamics. By − A it is denoted the infinitesimal generator of a C o-semigroup e − t A $${e}^{-tA}$$ , t ∈ ℝ + $$t \in {\mathbb{R}}^{+}$$ of operators acting on an ordered Hilbert space E and F : ℝ × E → E $$F: \mathbb{R} \times E \rightarrow E$$ is a given function. We also examine the case of the construction of positive almost periodic solutions.

Keywords: Evolution equation; Analytic semigroups; Strong and classical solutions; Ordered Banach spaces; Magneto-hydrodynamics; 34K30; 35R10; 47H07 (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-04720-1_3

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DOI: 10.1007/978-3-319-04720-1_3

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