We establish the local well-posedness of the modified Schrödinger map in H3/4+ε(R2).

In this article we study local and global well-posedness of the Lagrangian Averaged Euler equations. We show local well-posedness in TriebelLizorkin spaces and further prove a Beale-Kato-Majda type necessary and sufficient condition for global existence involving the stream function. We also establish new sufficient conditions for global existence in terms of mixed Lebesgue norms of the general...

the main purpose of this paper is to obtain sufficient conditions for existence of points of coincidence and common fixed points for three self mappings in $b$-metric spaces. next, we obtain cone $b$-metric version of these results by using a scalarization function. our results extend and generalize several well known comparable results in the existing literature.

− The problem of finding the greatest common divisor (GCD) of univariate polynomials appears in many engineering fields. Despite its formulation is well-known, it is an ill-posed problem that entails numerous difficulties when the coefficients of the polynomials are not known with total accuracy, as, for example, when they come from measurement data. In this work we propose a novel GCD estimati...

in this paper, we introduce the (g-$psi$) contraction in a metric space by using a graph.let $f,t$ be two multivalued mappings on $x.$ among other things, we obtain a common fixedpoint of the mappings $f,t$ in the metric space $x$ endowed with a graph $g.$

We investigate the solution of an N-unit series system with finite number of vacations. By using CC00-semigroup theory of linear operators, we prove well-posedness and the existence of the unique positive dynamic solution of the system.

Article history: Received 31 August 2015 Available online 27 February 2016 MSC: 35B34 35B35 35B40 35J05 78A25

We consider the Cauchy problem for the KdV equation with low regularity initial data given in the space Hs,a(R), which is defined by the norm ‖φ‖Hs,a = ‖〈ξ〉s−a|ξ|a b φ‖L2 ξ . We obtain the local well-posedness in Hs,a with s ≥ max{−3/4,−a − 3/2}, −3/2 < a ≤ 0 and (s, a) 6= (−3/4,−3/4). The proof is based on Kishimoto’s work [12] which proved the sharp well-posedness in the Sobolev space H−3/4(R...

In dimensions d ≥ 3, we prove that the Schrödinger map initialvalue problem { ∂ts = s×∆xs on R × R; s(0) = s0 is globally well-posed for small data s0 in the critical Besov spaces Ḃ d/2 Q (R ; S), Q ∈ S.