The Gevrey analyticity and decay for the micropolar system in the critical Besov space
type: Item
instance of: scholarly article
title: The Gevrey analyticity and decay for the micropolar system in the critical Besov space
zbMATH Open document ID: 1482.35013
author: Zihao Song
published in: Journal of Evolution Equations
publication date: 2022-01-06T00:00:00Z
review text: The author is interested in the 3-D incompressible micropolar fluid system in \(\mathbb R^+\times\mathbb R^3\): \[ \begin{cases} \partial_tu-(\chi+\nu)\Delta u+u\cdot\nabla u+\nabla\pi-2\chi\nabla\times\omega=0,\\ \partial_t\omega-\mu\Delta\omega+u\cdot\nabla\omega+4\chi\omega-\kappa\nabla\operatorname{div}\omega-2\chi\nabla\times u=0,\\ \operatorname{div}u=0,\\ (u,\omega)_{|t=0}=(u_0,\omega_0), \end{cases} \] where \(u = u(x, t)\) denotes the fluid velocity, \(\omega(x, t)\) denotes the velocity field of rotation for the particle of the fluid, \(\pi(x, t)\) represents the scalar pressure, \(\nu\) denotes the Newtonian kinematic viscosity, \(\chi\) denotes the micro-rotation viscosity, and where \(\kappa,\mu\) are the angular viscosities. He first proves the global in-time existence of the strong solutions in the Besov spaces \(\dot{B}_{p,q}^{\frac{3}{p}-1}\) with \(1\leq p<\infty\) and \(1\leq q\leq\infty\). Then, he establishes the global Gevrey analyticity in these spaces and the time-decay estimates on any derivatives of the solutions for large time. To do that, the approach developed by the author is inspired, on one hand, by the work of \textit{J.-Y. Chemin} [J. Anal. Math. 77, 27--50 (1999; Zbl 0938.35125)] and, on the other hand, by the work of \textit{H. Bae} et al. [Arch. Ration. Mech. Anal. 205, No. 3, 963--991 (2012; Zbl 1317.76029)] for the incompressible Navier-Stokes equations.
reviewed by: Pascal Remy
Mathematics Subject Classification ID: 35A20
Mathematics Subject Classification ID: 35K45
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 39A14
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 46N20
Mathematics Subject Classification ID: 76A05
zbMATH DE Number: 7452686
zbMATH Keywords: critical Besov space
zbMATH Keywords: micropolar system
zbMATH Keywords: Gevrey analyticity
MaRDI profile type: Publication
full work available at URL: s00028-021-00731-0
OpenAlex ID: W3183092047
cites work: Analyticity and decay estimates of the Navier-Stokes equations in critical Besov spaces
cites work: Fourier Analysis and Nonlinear Partial Differential Equations
cites work: Ill-posedness of the Navier-Stokes equations in a critical space in 3D
cites work: Smooth or singular solutions to the Navier-Stokes system?
cites work: A generalization of a theorem by Kato on Navier-Stokes equations
cites work: Q4223061
cites work: Gevrey analyticity and decay for the compressible Navier-Stokes system with capillarity
cites work: Q5316239
cites work: Uniqueness theorems for the three dimensional Navier-Stokes system
cites work: Flows of non-Lipschitzian vector fields and Navier-Stokes equations
cites work: Global well-posedness for the micropolar fluid system in critical Besov spaces
cites work: Global well-posedness of the 2D incompressible micropolar fluid flows with partial viscosity and angular viscosity
cites work: Q5283769
cites work: Global well-posedness and large-time decay for the 2D micropolar equations
cites work: Global regularity for the 2D micropolar equations with fractional dissipation
cites work: Global regularity of the 2D micropolar fluid flows with zero angular viscosity
cites work: Micropolar fluid system in a space of distributions and large time behavior
cites work: On the Navier-Stokes initial value problem. I
cites work: A note on the existence and uniqueness of solutions of the micropolar fluid equations
cites work: Existence of global strong solutions in critical spaces for barotropic viscous fluids
cites work: Well-posedness for the Navier-Stokes equations
cites work: Micropolar fluids. Theory and applications
cites work: Q5607484
cites work: Ill-posedness for the Navier-Stokes equations in critical Besov spaces \(\dot{B}_{\infty, q}^{- 1}\)
cites work: Ill-posedness of the 3D-Navier-Stokes equations in a generalized Besov space near \(\mathrm{BMO}^{-1}\)
cites work: On regularity criteria for weak solutions to the micropolar fluid equations in Lorentz space
cites work: Blow-up criteria of smooth solutions to the three-dimensional micropolar fluid equations in Besov space
cites work: Regularizing rate estimates for the 3-D incompressible micropolar fluid system in critical Besov spaces
cites work: The optimal temporal decay estimates for the micropolar fluid system in negative Fourier-Besov spaces
DOI: 10.1007/S00028-021-00731-0
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description: scientific article; zbMATH DE number 7452686