We consider the derivation of defocusing cubic nonlinear Schrödinger equation (NLS) on $${\mathbb {R}}^{3}$$ from quantum N-body dynamics. reformat hierarchy approach with Klainerman-Machedon theory and prove a bi-scattering theorem for NLS to obtain convergence rate estimates under $$H^{1}$$ regularity. The estimate we is almost optimal datum, immediately improves if have any extra regularity ...

We consider the three-dimensional incompressible free-boundary magnetohydrodynamics (MHD) equations in a bounded domain with surface tension on boundary. establish priori estimate for solutions Lagrangian coordinates $H^{3.5}$ regularity. To best of our knowledge, this is first result focusing ideal MHD tension. It worth pointing out that $1/2$-extra spatial regularity flow map $\eta$ no longer...

We present and analyze novel hierarchical a posteriori error estimates for self-adjoint elliptic obstacle problems. Our approach differs from straightforward, but nonreliable estimators by an additional extra term accounting for the deviation of the discrete free boundary in the localization step. We prove efficiency and reliability on a saturation assumption and a regularity condition on the u...

In this paper we study the fully nonlinear free boundary problem { F (Du) = 1 a.e. in B1 ∩ Ω |Du| ≤ K a.e. in B1 \ Ω, where K > 0, and Ω is an unknown open set. Our main result is the optimal regularity for solutions to this problem: namely, we prove that W 2,n solutions are locally C inside B1. Under the extra condition that Ω ⊃ {Du 6= 0} and a uniform thickness assumption on the coincidence s...

We consider the vorticity-stream formulation of axisymmetric incompressible flows and its equivalence with the primitive formulation. It is shown that, to characterize the regularity of a divergence free axisymmetric vector field in terms of the swirling components, an extra set of pole condition is necessary to give a full description of the regularity. In addition, smooth solutions up to the ...

In this paper, first we introduce the notions of an $(m,n)$-hyperideal and a generalized $(m,n)$-hyperideal in an ordered semihypergroup, and then, some properties of these hyperideals are studied. Thereafter, we characterize $(m,n)$-regularity, $(m,0)$-regularity, and $(0,n)$-regularity of an ordered semihypergroup in terms of its $(m,n)$-hyperideals, $(m,0)$-hyperideals and $(0,n)$-hyperideal...

the main concern of the present study was to compare the frequency of the use of semantic adjustment strategies in versed and free-verse styles in the english translations of hafez poetry. the focus of the comparison was the number of expansion and reduction strategies employed in these translations. the corpus of the study comprised two translations of hafez poetry; one was a versed translatio...

In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain ...

In this paper we consider the fully nonlinear parabolic free boundary problem { F (Du)− ∂tu = 1 a.e. in Q1 ∩ Ω |Du|+ |∂tu| ≤ K a.e. in Q1 \ Ω, where K > 0 is a positive constant, and Ω is an (unknown) open set. Our main result is the optimal regularity for solutions to this problem: namely, we prove that W 2,n x ∩W 1,n t solutions are locally C 1,1 x ∩C 0,1 t inside Q1. A key starting point for...