Non-uniform dependence on initial data for the periodic Degasperis-Procesi equation

In this paper, we show that the solution map of the periodic Degasperis-Procesi equation is not uniformly continuous in Sobolev spaces Hs(T) for s>3/2. This extends previous result for s?2 to the whole range of s for which the local well-posedness is known. Our proof is based on the method of approximate solutions and well-posedness estimates for the actual solutions.     

Global well-posedness for Keller-Segel system in Besov type spaces

The Cauchy problems for Keller-Segel system are studied using homogeneous Besov spaces. With the homogeneous Besov spaces , which is the scaling critical case for Keller-Segel system, global solutions for small initial data are obtained in the space. In addition, ill-posedness for Keller-Segel system is also studied.     

Weakly singular initial values for the Stokes equation on a half space

We study the extension of Ukai's formula to the case of singular initial values for the Stokes problem on the half space.     

Well-posedness for the Navier-Stokes-Nernst-Planck-Poisson system in Triebel-Lizorkin space and Besov space with negative indices

This paper is concerned with the well-posedness of the Navier-Stokes-Nerst-Planck-Poisson system (NSNPP). Let sp=−2+n/p. We prove that the NSNPP has a unique local solution for in a subspace, i.e., Vu1×Vv1×Vv1, of with . We also prove that there exists a unique small global solution for any small initial data with .     

Local solvability of the Keller–Segel system with Cauchy data in the Besov spaces

The Cauchy problem for the Keller–Segel system of parabolic elliptic type is considered for initial data in the Besov spaces with p < ∞ , and a sufficient condition is given on the existence and the uniqueness of local solutions. Copyright © 2013 John Wiley & Sons, Ltd.     

On the Cauchy problem for the fractional drift-diffusion system in critical Besov spaces

In this paper, we establish global well-posedness and asymptotic stability of mild solutions for the Cauchy problem of the fractional drift-diffusion system with small initial data in critical Besov spaces. The regularizing-decay rate estimates of mild solutions are also proved, which imply that mild solutions are analytic in space variables.     

d-集上的Besov空间的一个迹定理

In the paper we give a trace theorem of Besov spaces Bαp,p(Rn) on a d-set.It is a kind of extension of related results of Jonsson and Wallin,which has important applications on PDE theory.     

Sharp Estimates in Bergman and Besov Spaces on Bounded Symmetric Domains

Sharp estimates of the point-evaluation functional in weighted Bergman spaces L ^p _a (Ω, dν _α) and for the point-evaluation derivalive functional in Besov spaces B ^p (Ω) are obtained for bounded symmetric domains Ω in ℂ ⁿ . Received October 25, 1999, Accepted December 6, 2000     

Nonstationary Stokes system in Besov spaces

We examine the solvability in Besov spaces of an initial–boundary value problem for the nonstationary Stokes system with the slip boundary conditions. We prove the existence and uniqueness of solutions to the problem in a bounded domain . The existence is shown by localizing the system to interior and boundary subdomains of Ω. The localized Stokes system is transformed by the Helmholtz–Weyl decomposition to the heat and the Poisson equations, which are solved in the Besov spaces. Next, by the properties of the partition of unity and a perturbation argument, the existence is proved in domain Ω. Copyright © 2013 John Wiley & Sons, Ltd.     

The low Mach number limit in Besov spaces for compressible magnetohydrodynamics equations

In this paper, we develop a continuation principle for general hyperbolic singular limit problems in more general Besov spaces, which covers the cases of usual Sobolev spaces with higher regularity in and the critical Besov space. As an application, we give a simple justification for the low Mach number limit of compressible magnetohydrodynamics equations. More precisely, for the Mach number sufficiently small, the smooth compressible flows exist on the (finite) time interval where the incompressible magnetohydrodynamics equations have smooth solutions, and the definite convergence orders are also obtained. Copyright © 2014 John Wiley & Sons, Ltd.     

Regularity estimates for elliptic boundary value problems in Besov spaces

We consider the Dirichlet problem for Poisson's equation on a nonconvex plane polygonal domain . New regularity estimates for its solution in terms of Besov and Sobolev norms of fractional order are proved. The analysis is based on new interpolation results and multilevel representations of norms on Sobolev and Besov spaces. The results can be extended to a large class of elliptic boundary value problems. Some new sharp finite element error estimates are deduced.

     

Commutators for Fourier multipliers on Besov Spaces

If T is any bounded linear operator on Besov spaces B_p^σ_j,q_j(Rⁿ)(j=0,1, and 0<σ₁<σ<σ₀), it is proved that the commutator [T,T_μ]=TT_μ−T_μT is bounded on B_p^σ,q(Rⁿ), if T_μ is a Fourier multiplier such that μ is any (possibly unbounded) symbol with uniformly bounded variation on dyadic coronas.     

On the regularity criterion for three-dimensional micropolar fluid flows in Besov spaces

This paper studies the regularity criterion of weak solutions for three-dimensional (3D) micropolar fluid flows. When the velocity field satisfies for −1<r<1, then the weak solution (u,w) is regular on (0,T]. The methods are mainly based on the Fourier localization technique and Bony’s para-product decomposition.