Existence of solutions to the nonstationary Stokes system in $H_{-μ}^{2,1}$, μ ∈ (0,1), in a domain with a distinguished axis. Part 2. Estimate in the 3d case

• Autorzy: W. M. Zajączkowski
• Języki publikacji: EN

Abstrakty

EN

We examine the regularity of solutions to the Stokes system in a neighbourhood of the distinguished axis under the assumptions that the initial velocity v₀ and the external force f belong to some weighted Sobolev spaces. It is assumed that the weight is the (-μ )th power of the distance to the axis. Let $f∈ L_{2,-μ}$, $v₀ ∈ H_{-μ}¹$, μ ∈ (0,1). We prove an estimate of the velocity in the $H_{-μ}^{2,1}$ norm and of the gradient of the pressure in the norm of $L_{2,-μ}$. We apply the Fourier transform with respect to the variable along the axis and the Laplace transform with respect to time. Then we obtain two-dimensional problems with parameters. Deriving an appropriate estimate with a constant independent of the parameters and using estimates in the two-dimensional case yields the result. The existence and regularity in a bounded domain will be shown in another paper.

Kategorie tematyczne

• 76D03: Existence, uniqueness, and regularity theory
• 35Q30: Navier-Stokes equations
• 76D99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2007
• Tom: 34
• Numer: 2
• Strony: 143-167

Daty

wydano

2007

Twórcy

autor

W. M. Zajączkowski

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland
• Institute of Mathematics and Cryptology, Military University of Technology, Kaliskiego 2, 00-908 Warszawa, Poland

Identyfikatory

DOI

10.4064/am34-2-2