Global well-posedness for Navier-Stokes equations with small initial value in \(B^{0}_{n,\infty}(\Omega)\)

DOI10.1007/s00021-015-0243-4zbMath1334.35209OpenAlexW2264435817MaRDI QIDQ270183

Zhifei Zhang, Myong-Hwan Ri, Ping Zhang

Publication date: 7 April 2016

Published in: Journal of Mathematical Fluid Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00021-015-0243-4

zbMATH Keywords

existenceNavier-Stokes equationsuniquenessStokes operatormaximal regularity

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Stability in context of PDEs (35B35) Stokes and related (Oseen, etc.) flows (76D07) Navier-Stokes equations (35Q30) Hydrodynamic stability (76E99)

Related Items (9)

Maximal \(L^1\)-regularity of generators for bounded analytic semigroups in Banach spaces ⋮ Global in time solvability of the Navier-Stokes equations in the half-space ⋮ Global well-posedness for inhomogeneous Navier-Stokes equations in endpoint critical Besov spaces ⋮ A note on the \(3\)-D Navier-Stokes equations ⋮ Initial-boundary value problem of the Navier-Stokes equations in the half space with nonhomogeneous data ⋮ Existence of incompressible and immiscible flows in critical function spaces on bounded domains ⋮ Global well-posedness of the half space problem of the Navier-Stokes equations in critical function spaces of limiting case ⋮ On critical spaces for the Navier-Stokes equations ⋮ Regularity criteria for 3D Navier-Stokes equations in terms of finite frequency parts of velocity in \(\dot{B}_{\infty, \infty}^{- 1} \)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Strong \(L^ p\)-solutions of the Navier-Stokes equation in \(R^ m\), with applications to weak solutions
• Optimal initial value conditions for the existence of local strong solutions of the Navier-Stokes equations
• Resolvent estimates for the Stokes operator on an infinite layer.
• Ill-posedness of the Navier-Stokes equations in a critical space in 3D
• Resolvent estimates and maximal regularity in weighted \(L^{q}\)-spaces of the Stokes operator in an infinite cylinder
• On optimal initial value conditions for local strong solutions of the Navier-Stokes equations
• Semigroups of linear operators and applications to partial differential equations
• Domains of fractional powers of the Stokes operator in \(L_ r\) spaces
• Solutions in \(L_ r\) of the Navier-Stokes initial value problem
• \(L^ 2\) decay for the Navier-Stokes flow in halfspaces
• On the semigroup of the Stokes operator for exterior domains in L q- spaces
• Parabolic evolution equations in interpolation and extrapolation spaces
• Equations d'évolution abstraites non linéaires de type parabolique
• Analyticity of the semigroup generated by the Stokes operator in \(L_r\) spaces
• On nonstationary solutions of the Navier-Stokes equations in an exterior domain
• Abstract \(L^ p\) estimates for the Cauchy problem with applications to the Navier-Stokes equations in exterior domains
• The Navier-Stokes equations -- a neverending challenge?
• Center manifolds for quasilinear reaction-diffusion systems
• A generalization of a theorem by Kato on Navier-Stokes equations
• On a resolvent estimate of the Stokes equation on an infinite layer.
• On the strong solvability of the Navier-Stokes equations
• On the closedness of the sum of two closed operators
• Maximal regularity for evolution equations in weighted \(L_p\)-spaces
• On the Navier-Stokes initial value problem. I
• The resolvent problem and \(H^\infty\)-calculus of the Stokes operator in unbounded cylinders with several exits to infinity
• Multipliers, paramultipliers, and weak-strong uniqueness for the Navier-Stokes equations
• An Introduction to the Mathematical Theory of the Navier-Stokes Equations
• Nonlinear analytic semiflows
• ℛ-boundedness, Fourier multipliers and problems of elliptic and parabolic type
• Strong Solutions To The Incompressible Navier Stokes Equations In The Half Space
• Self-similar solutions for navier-stokes equations in
• Regularity of Solutions to the Navier-Stokes Equations Evolving from Small Data in BMO−1
• Well-posedness for the Navier-Stokes equations
• Maximal regularity in continuous interpolation spaces and quasilinear parabolic equations
• \(L^p\)-theory of the Stokes equation in a half space

This page was built for publication: Global well-posedness for Navier-Stokes equations with small initial value in \(B^{0}_{n,\infty}(\Omega)\)