The Stokes Equations: Vol 76 (Mathematical research) - Softcover

Varnhorn, Werner

Softcover

ISBN 10: 3055016343 ISBN 13: 9783055016349

Verlag: Wiley-VCH Verlag GmbH, 1994

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In the first part of this text a theory of solvability for the stationary Stokes equations in exterior domains is developed. Varnhorn proves the existence of strong solutions in Sobolev spaces and uses a localization principle and the divergence equation to deduce further properties of the solution (uniqueness, asymptotics). The second part considers the resolvent equations with methods of potential theory. The author presents the explicit fundamental tensor for general space dimension and solves the boundary value problems via systems of integral equations. New a-priori norm estimates for the solution are developed independently of small resolvent parameters. This leads to the uniform boundedness of the semigroup associated with the Stokes operator, also for the case of a two-dimensional exterior domain. In the third part Varnhorn approximates the nonstationary equations with help of the resolvent and proves convergence of optimal order in a scale of Sobolev spaces. This includes the nonlinear Navier-Stokes equations, which can be regularized with methods of time delay.

Über diese Auflage

• Verlag: Wiley-VCH Verlag GmbH
• Erscheinungsdatum: 1994
• ISBN 10: 3055016343
• ISBN 13: 9783055016349
• Einband: Tapa blanda
• Anzahl der Seiten: 154