Uniform global solvability of the rotating Navier-Stokes equations for nondecaying initial data

Giga, Yoshikazu; Inui, Katsuya; Mahalov, Alex; Saal, Jürgen

Uniform global solvability of the rotating Navier-Stokes equations for nondecaying initial data

Files

research_paper_253.pdf(409.83 KB)

Date

2008

Authors

Giga, Yoshikazu

Inui, Katsuya

Mahalov, Alex

Saal, Jürgen

Series

Konstanzer Schriften in Mathematik und Informatik; 253

Publication type

Preprint

Abstract

We establish a global existence result for the rotating Navier-Stokes equations with nondecaying initial data in a critical space which includes a large class of almost periodic functions. The scaling invariant function space we introduce is given as the divergence of the space of 3x3 fields of Fourier transformed finite Radon measures. The smallness condition on initial data for global existence is explicitly given in terms of the Reynolds number. The condition is independent of the size of the angular velocity of rotation.

Summary in another language

In einem kritischen Funktionenraum, der eine große Klasse fast-periodischer Funktionen enhält, wird die Existenz von globalen Lösungen nachgewiesen. Der skalierungsinvariante Funtionenraum ergibt sich als Divergenz der 3x3 Vektorfelder von Fouriertransformierten endlichen Radonmaßen. Die Kleinheitsbedingung an den Anfangswert für globale Existenz ist explizit durch die Reynoldszahl dargestellt. Diese Bedingung ist unabhängig von der Winkelgeschwindigkeit der Rotation.

Subject (DDC)

510 Mathematics

Keywords

Navier-Stokes-Gleichungen mit Rotation,globale Lösungen,rotating Navier-Stokes equations,global solvability

Cite This

ISO 690

GIGA, Yoshikazu, Katsuya INUI, Alex MAHALOV, Jürgen SAAL, 2008. Uniform global solvability of the rotating Navier-Stokes equations for nondecaying initial data

BibTex

@unpublished{Giga2008Unifo-647,
  year={2008},
  title={Uniform global solvability of the rotating Navier-Stokes equations for nondecaying initial data},
  author={Giga, Yoshikazu and Inui, Katsuya and Mahalov, Alex and Saal, Jürgen}
}

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