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Maximal regularity and viscous incompressible flows with free interface

100%

Shimizu S.

Banach Center Publications

2008

tom 81

nr 1

471-480

We consider a free interface problem for the Navier-Stokes equations. We obtain local in time unique existence of solutions to this problem for any initial data and external forces, and global in time unique existence of solutions for sufficiently small initial data. Thanks to global in time $L_{p} - L_{q}$ maximal regularity of the linearized problem, we can prove a global in time existence and uniqueness theorem by the contraction mapping principle.

On the Stokes equation with Neumann boundary condition

63%

Shibata Y., Shimizu S.

Banach Center Publications

2005

tom 70

nr 1

239-250

In this paper, we study the nonstationary Stokes equation with Neumann boundary condition in a bounded or an exterior domain in ℝⁿ, which is the linearized model problem of the free boundary value problem. Mainly, we prove $L_p - L_q$ estimates for the semigroup of the Stokes operator. Comparing with the non-slip boundary condition case, we have the better decay estimate for the gradient of the semigroup in the exterior domain case because of the null force at the boundary.

Ograniczanie wyników

2 Banach Center Publications

2 Shimizu S.

1 Shibata Y.

1 2008

1 2005

Wyniki wyszukiwania

Maximal regularity and viscous incompressible flows with free interface

On the Stokes equation with Neumann boundary condition