Estimates for solutions of the nonstationary Stokes problem in anisotropic Sobolev spaces with mixed norm

DOI10.1007/BF02355828zbMath0909.35105MaRDI QIDQ1376854

Paolo Maremonti, Vsevolod A. Solonnikov

Publication date: 15 March 1999

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/68571

zbMATH Keywords

Stokes problem\(L_{q,r}\)-estimatesestimates of heat potentials

Mathematics Subject Classification ID

Navier-Stokes equations (35Q30) A priori estimates in context of PDEs (35B45)

Related Items (17)

Unnamed Item ⋮ New version of the Ladyzhenskaya–Prodi–Serrin condition ⋮ Gradient estimates in anisotropic Lorentz spaces to general elliptic equations of \(p\)-growth ⋮ On the Stokes problem in exterior domains: the maximum modulus theorem ⋮ On the Navier-Stokes problem in exterior domains with non decaying initial data ⋮ Non-decaying solutions to the Navier Stokes equations in exterior domains ⋮ Mixed-norm \(L_p\)-estimates for non-stationary Stokes systems with singular VMO coefficients and applications ⋮ On weak \(D\)-solutions to the non-stationary Navier-Stokes equations in a three-dimensional exterior domain ⋮ Parabolic equations with VMO coefficients in Sobolev spaces with mixed norms ⋮ Estimates of anisotropic Sobolev spaces with mixed norms for the Stokes system in a half-space ⋮ The Navier-Stokes equations in the critical Lebesgue space ⋮ Solvability of parabolic equations in divergence form with partially BMO coefficients ⋮ On smoothness of \(L_{3,\infty}\)-solutions to the Navier-Stokes equations up to boundary ⋮ Conditional stability and periodicity of solutions to evolution equations ⋮ Rubio de Francia extrapolation theorem and related topics in the theory of elliptic and parabolic equations. A survey ⋮ Boundary partial regularity for the Navier-Stokes equations ⋮ Nonstationary Stokes equations in a half-space with continuous initial data

Cites Work

• \(L_ q-L_ r\) estimates for solutions of the nonstationary Stokes equation in an exterior domain and the Navier-Stokes initial value problems in \(L_ q\) spaces
• Abstract \(L^ p\) estimates for the Cauchy problem with applications to the Navier-Stokes equations in exterior domains
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