End-point maximal regularity and its application to two-dimensional Keller-Segel system

DOI10.1007/s00209-009-0481-3zbMath1198.35045OpenAlexW2017774519MaRDI QIDQ848829

Senjo Shimizu, Takayoshi Ogawa

Publication date: 23 February 2010

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-009-0481-3

zbMATH Keywords

homogeneous Besov space

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Maximal functions, Littlewood-Paley theory (42B25) Interpolation between normed linear spaces (46B70) Initial value problems for second-order parabolic equations (35K15)

Related Items (34)

Maximal \(L^1\)-regularity for parabolic initial-boundary value problems with inhomogeneous data ⋮ End-point maximal \(L^1\)-regularity for the Cauchy problem to a parabolic equation with variable coefficients ⋮ Local and global solvability for Keller-Segel system in Besov-Morrey spaces ⋮ Well-posedness and Gevrey analyticity of the generalized Keller-Segel system in critical Besov spaces ⋮ The semigroup generated by the Dirichlet Laplacian of fractional order ⋮ Maximal regularity of the heat evolution equation on spatial local spaces and application to a singular limit problem of the Keller-Segel system ⋮ Singular limit problem for the Keller-Segel system and drift-diffusion system in scaling critical spaces ⋮ Global well-posedness of the Navier-Stokes equations in homogeneous Besov spaces on the half-space ⋮ Singular limit problem for the Keller-Segel system and drift-diffusion system in scaling critical Besov-Morrey spaces ⋮ Maximal regularity for the Cauchy problem of the heat equation in BMO ⋮ Complex valued semi-linear heat equations in super-critical spaces \(E^s_\sigma\) ⋮ A characterization of \(L^p\)-maximal regularity for time-fractional systems in \textit{UMD} spaces and applications ⋮ Maximal \(L^1\)-regularity for parabolic boundary value problems with inhomogeneous data in the half-space ⋮ Global existence of large solutions for the parabolic-elliptic Keller-Segel system in Besov type spaces ⋮ Global solution to the Cauchy problem of fractional drift diffusion system with power-law nonlinearity ⋮ Global existence and temporal decay of large solutions for the Poisson–Nernst–Planck equations in low regularity spaces ⋮ Existence and uniqueness theorem on weak solutions to the parabolic-elliptic Keller-Segel system ⋮ Existence of solutions for the Debye-Hückel system with low regularity initial data ⋮ Singular limit for the magnetohydrodynamics of the damped wave type in the critical Fourier-Sobolev space ⋮ Global well-posedness for the incompressible Navier-Stokes equations in the critical Besov space under the Lagrangian coordinates ⋮ Regularity estimates for the Cauchy problem to a parabolic equation associated to fractional harmonic oscillators ⋮ On the maximal regularity for perturbed autonomous and non-autonomous evolution equations ⋮ The drift-diffusion system in two-dimensional critical Hardy space ⋮ Global existence of large solutions for the generalized Poisson-Nernst-Planck equations ⋮ Global well-posedness for Keller-Segel system in Besov type spaces ⋮ Local solvability of the Keller–Segel system with Cauchy data in the Besov spaces ⋮ Gevrey regularity of mild solutions to the parabolic-elliptic system of drift-diffusion type in critical Besov spaces ⋮ Asymptotic stability of stationary solutions to the drift-diffusion model with the fractional dissipation ⋮ The optimal temporal decay estimates for the fractional power dissipative equation in negative Besov spaces ⋮ Maximal \(L^1\)-regularity of the heat equation and application to a free boundary problem of the Navier-Stokes equations near the half-space ⋮ Maximal regularity and a singular limit problem for the Patlak-Keller-Segel system in the scaling critical space involving \textit{BMO} ⋮ Maximal Lorentz regularity for the Keller-Segel system of parabolic-elliptic type ⋮ Singular limit problem for the two-dimensional Keller-Segel system in scaling critical space ⋮ On the Cauchy problem for the fractional drift-diffusion system in critical Besov spaces

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