We study the well-posedness and regularity of the generalized Navier-Stokes equations with initial data in a new critical space Q α;∞ (R ) = ∇ · (Qα(R )), β ∈ ( 1 2 , 1) which is larger than some known critical homogeneous Besov spaces. Here Qα(R ) is a space defined as the set of all measurable functions with sup(l(I)) Z

We note a sharp embedding of the Besov space B∞ 0,q(T) into exponential classes and prove entropy estimates for the compact embedding of subclasses with logarithmic smoothness, considered by Kashin and Temlyakov.

A small perturbation method is developed and deployed to the construction of frames with compactly supported elements of small shrinking supports for Besov and Triebel-Lizorkin spaces in the general setting of a doubling metric measure space in presence of a non-negative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. This allows, in particular, to dev...

We consider Bayesian approach to wavelet decomposition. We show how prior knowledge about a function's regularity can be incorporated into a prior model for its wavelet coeecients by establishing a relationship between the hyperparameters of the proposed model and the parameters of those Besov spaces within which realizations from the prior will fall. Such a relation may be seen as giving insig...

We show that the wave map equation in R is in general illposed in the critical space Ḣ1/2, and the Besov space Ḃ 1/2,1 2 . The problem is attributed to the bad behaviour of the one-dimensional bilinear expression D(fDg) in these spaces.

Without any smallness assumption, we prove the global unique solvability of 2-D incompressible inhomogeneous Navier-Stokes equations with initial data in critical Besov space, which is almost energy space sense that they have same scaling terms this system.

We study the Cauchy singular integral operator SwI on (−1, 1), where |w| is a generalized Jacobi weight. This operator is considered in pairs of weighted spaces of continuous functions, where the weights u and v are generalized Jacobi weights with nonnegative exponents such that |w| = u/v. We introduce a certain polynomial approximation space which is well appropriated to serve as domain of def...

Decomposition spaces are a class of function constructed out “well-behaved” coverings and partitions unity set. The structure the covering determines properties decomposition space. Besov spaces, shearlet mo

In this article, we show that the magneto-hydrodynamic system (MHD) in R with variable density, variable viscosity and variable conductivity has a local weak solution in the Besov space Ḃ N p1 p1,1 (R )×Ḃ N p2 −1 p2,1 (R )×Ḃ N p2 −1 p2,1 (R ) for all 1 < p2 < +∞ and some 1 < p1 ≤ 2N 3 if the initial density approaches a positive constant. Moreover, this solution is unique if we impose the restr...

This paper deals with approximation numbers of the compact trace operator of an anisotropic Besov space into some Lp-space, trΓ : B s,a pp (R ) ↪→ Lp(Γ), s > 0, 1 < p < ∞, where Γ is an anisotropic d-set, 0 < d < n. We also prove homogeneity estimates, a homogeneous equivalent norm and the localization property in B pp .