We show that the viscous resistive magnetohydrodynamics system with Hall effect is locally well-posed in Hs(R3)×Hs+1??(R3) s>12 and any small enough ?>0 such s??>12. This space to date largest local well-posedness class of Sobolev spaces for system. It also optimal according predominant scalings two equations

Summary In Brazil, high-yield soybean [ Glycine Max (L). Merrill] – corn ( Zea mays L.) double cropping system might be nitrogen (N)-limited and additional N fertilization can beneficial. Early application of in reduces the symbiotic fixation (SNF) efficiency and/or establishment. One alternative to avoid SNF impairment is apply between beginning pod (R3) seed-fill (R5) stages through use contr...

As important parameters in the characterization of aerobic granulation, shape and average diameter were related to substrates. The previous studies disclosed that morphology change granules was result growth relatively strong hydrodynamic shear force. No further exploration size distribution has been conducted. To better understand impact toxic compounds on granules’ during their formation, pro...

We prove that there exists a universal constant r3 such that if X is a smooth projective threefold overCwith non-negative Kodaira dimension, then the linear system |rKX | admits a fibration that is birational to the Iitaka fibration as soon as r ≥ r3 and sufficiently divisible. This gives an affirmative answer to a conjecture of Hacon and McKernan [5, Conjecture 1.7] in the case of threefolds.

In this article we prove a collection of new non-linear and non-local integral inequalities. As an example for u ≥ 0 and p ∈ (0,∞) we obtain ∫ R3 dx u(x) ≤ ( p+ 1 p )2 ∫ R3 dx {(−4)−1u(x)}|∇u p 2 (x)|. We use these inequalities to deduce global existence of solutions to a non-local heat equation with a quadratic non-linearity for large radial monotonic positive initial conditions. Specifically,...

In this paper we study the nonlinear Schrödinger-Maxwell equations { −∆u+ V (x)u+ φu = |u|p−1u in R3, −∆φ = u2 in R3. If V is a positive constant, we prove the existence of a ground state solution (u, φ) for 2 < p < 5. The non-constant potential case is treated under suitable geometrical assumptions on V , for 3 < p < 5. Existence and non-existence results are proved also when the nonlinearity ...

This paper intends to study the following degenerate fractional Schrödinger–Kirchhoff–Poisson equations with critical nonlinearity and electromagnetic fields in R3: {ε2sM([u]s,A2)(−Δ)Asu+V(x)u+ϕu=k(x)|u|r−2u+(Iμ∗|u|2s♯)|u|2s♯−2u,x∈R3,(−Δ)tϕ=u2,x∈R3, where ε>0 is a positive parameter, 3/4<s<1, 0<t<1, V an electric potential satisfying suitable assumptions, 0<k∗≤k(x)≤k∗, Iμ(x)=|x|3−μ 0<μ<3, 2s♯=3...