Displaying similar documents to “Analycity of the Semigroup Generated by the Stokes Operator.”

A stability theorem of the Navier-Stokes flow past a rotating body

Yoshihiro Shibata (2008)

Banach Center Publications

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In this paper, a stability theorem of the Navier-Stokes flow past a rotating body is reported. Concerning the linearized problem, the proofs of the generation of a C₀ semigroup and its decay properties are sketched.

On the Stokes and Navier-Stokes flows in a perturbed half-space

Takayuki Kubo, Yoshihiro Shibata (2005)

Banach Center Publications

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We give the L p - L q estimate for the Stokes semigroup in a perturbed half-space and some global in time existence theorems for small solutions to the Navier-Stokes equation.

On the Stokes equation with Neumann boundary condition

Yoshihiro Shibata, Senjo Shimizu (2005)

Banach Center Publications

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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.

Navier-Stokes equations on unbounded domains with rough initial data

Peer Christian Kunstmann (2010)

Czechoslovak Mathematical Journal

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We consider the Navier-Stokes equations in unbounded domains Ω ⊆ ℝ n of uniform C 1 , 1 -type. We construct mild solutions for initial values in certain extrapolation spaces associated to the Stokes operator on these domains. Here we rely on recent results due to Farwig, Kozono and Sohr, the fact that the Stokes operator has a bounded H ∞ -calculus on such domains, and use a general form of Kato’s method. We also obtain information on the corresponding pressure term.