Proceedings of the Japan Academy, Series A, Mathematical Sciences

$L_p$-$L_q$ maximal regularity and viscous incompressible flows with free surface

Yoshihiro Shibata and Senjo Shimizu

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We prove the $L_p$-$L_q$ maximal regularity of solutions to the Neumann problem for the Stokes equations with non-homogeneous boundary condition and divergence condition in a bounded domain. And as an application, we consider a free boundary problem for the Navier-Stokes equation. We prove a locally in time unique existence of solutions to this problem for any initial data and a globally in time unique existence of solutions to this problem for some small initial data.

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Proc. Japan Acad. Ser. A Math. Sci., Volume 81, Number 9 (2005), 151-155.

First available in Project Euclid: 5 December 2005

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Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 76D05: Navier-Stokes equations [See also 35Q30]

Stokes equations Neumann boundary condition maximal regularity Navier-Stokes equations free boundary problem


Shibata, Yoshihiro; Shimizu, Senjo. $L_p$-$L_q$ maximal regularity and viscous incompressible flows with free surface. Proc. Japan Acad. Ser. A Math. Sci. 81 (2005), no. 9, 151--155. doi:10.3792/pjaa.81.151.

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