On an existence theorem for the Navier-Stokes equations with free slip boundary condition in exterior domain

• Autorzy: Rieko Shimada , Norikazu Yamaguchi
• Języki publikacji: EN

Abstrakty

EN

This paper deals with a nonstationary problem for the Navier-Stokes equations with a free slip boundary condition in an exterior domain. We obtain a global in time unique solvability theorem and temporal asymptotic behavior of the global strong solution when the initial velocity is sufficiently small in the sense of Lⁿ (n is dimension). The proof is based on the contraction mapping principle with the aid of $L^{p} - L^{q}$ estimates for the Stokes semigroup associated with a linearized problem, which is also discussed. In particular, we mainly discuss the local energy decay property of the semigroup which is a key estimate to prove the $L^{p} - L^{q}$ estimates in an exterior domain.

Kategorie tematyczne

• 76D05: Navier-Stokes equations
• 35Q30: Navier-Stokes equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2008
• Tom: 81
• Numer: 1
• Strony: 457-470

Daty

wydano

2008

Twórcy

autor

Rieko Shimada

• Department of Mathematical Sciences, School of Science and Engineering, Waseda University, 3-4-1 Ōkubo, Shinjuku-ku, Tokyo 169-8555, Japan

autor

Norikazu Yamaguchi

• Department of Mathematical Sciences, School of Science and Engineering, Waseda University, 3-4-1 Ōkubo, Shinjuku-ku, Tokyo 169-8555, Japan

Identyfikatory

DOI

10.4064/bc81-0-28