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Journal of Soviet Mathematics

, Volume 49, Issue 5, pp 1140–1147 | Cite as

Reduction of the fundamental initial-boundary-value problems for Stokes equations to initial-boundary-value problems for parabolic systems of pseudodifferential equations

  • G. Grubb
  • V. A. Solonnikov
Article

Abstract

It is shown that an initial-boundary-value problem for Stokes' system, in which on the boundary one prescribes the vector field of velocities\(\vec v\), or the stress field, or the normal component of the velocity and the tangential stresses, reduces to an initial-boundary-value problem for a system of the form\(\vec v_t + A\vec v = \vec f\), where the operator A contains a nonlocal term (the so-called singular Green operator). For the solutions of these problems, coercive estimates in the spaces W2l, l/2 and also estimates of the norm of the resolving operator in W2r are obtained.

Keywords

Vector Field Stress Field Stokes Equation Normal Component Tangential Stress 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • G. Grubb
  • V. A. Solonnikov

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