A priori estimates in terms of the maximum norm for the solutions of the Navier–Stokes equations

In this paper, we consider the Cauchy problem for the incompressible Navier–Stokes equations with bounded initial data and derive a priori estimates of the maximum norm of all derivatives of the solution in terms of the maximum norm of the initial velocity field. For illustrative purposes, we first...

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Bibliographic Details
Published inJournal of Differential Equations Vol. 203; no. 2; pp. 216 - 231
Main Authors Kreiss, Heinz–Otto, Lorenz, Jens
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.09.2004
Subjects
Incompressible Navier–Stokes equation
Maximum norm estimates
76D03
76D05
35Q30
Incompressible Navier–Stokes equation
Maximum norm estimates
35G25
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Summary:In this paper, we consider the Cauchy problem for the incompressible Navier–Stokes equations with bounded initial data and derive a priori estimates of the maximum norm of all derivatives of the solution in terms of the maximum norm of the initial velocity field. For illustrative purposes, we first derive corresponding a priori estimates for certain parabolic systems. Because of the pressure term, the case of the Navier–Stokes equations is more difficult, however.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2004.05.006