Strong solutions of the Landau-Lifshitz-Bloch equation in Besov space

We focus on the existence and uniqueness of the three-dimensional Landau-Lifshitz-Bloch equation supplemented with the initial data in Besov space $\dot{B}_{2,1}^{\frac{3}{2}}$. Utilizing a new commutator estimate, we establish the local existence and uniqueness of strong solutions for any initial data in $\dot{B}_{2,1}^{\frac{3}{2}}$. When the initial data is small enough in $\dot{B}_{2,1}^{\frac{3}{2}}$, we obtain the global existence and uniqueness. Furthermore, we also establish a blow-up criterion of the solution to the Landau-Lifshitz-Bloch equation and then we prove the global existence of strong solutions in Sobolev space under a new condition based on the blow-up criterion.Comment: 20 page

Weak solutions to the Hall-MHD equations whose singular sets in time have Hausdorff dimension strictly less than 1

In this paper, we focus on the three-dimensional hyper viscous and resistive Hall-MHD equations on the torus, where the viscous and resistive exponent $\alpha\in [\rho, 5/4)$ with a fixed constant $\rho\in (1,5/4)$. We prove the non-uniqueness of a class of weak solutions to the Hall-MHD equations, which have bounded kinetic energy and are smooth in time outside a set whose Hausdorff dimension strictly less than 1. The proof is based on the construction of the non-Leray-Hopf weak solutions via a convex integration scheme.Comment: 39 page

Global existence of strong solutions to the Landau-Lifshitz-Slonczewski equation

In this paper, we focus on the existence of strong solutions for the Cauchy problem of the three-dimensional Landau-Lifshitz-Slonczewski equation. We construct a new combination of Bourgain space and Lebesgue space where linear and nonlinear estimates can be closed by applying frequency decomposition and energy methods. Finally, we establish the existence and uniqueness of the global strong solution provided that the initial data belongs to Besov space $\dot{B}^{\frac{n}{2}}_{\Omega}$.Comment: 24 page

Derivation of the Hall-MHD equations from the Navier-Stokes-Maxwell equations

By using a set of scaling limits, the authors in \cite{ADFL,SS} proposed a framework of deriving the Hall-MHD equations from the two-fluids Euler-Maxwell equations for electrons and ions. In this paper, we derive the Hall-MHD equations from the Navier-Stokes-Maxwell equations with generalized Ohm's law in a mathematically rigorous way via the spectral analysis and energy methods

Retraction Note to: Global strong solution to the three-dimensional stochastic incompressible magnetohydrodynamic equations

The authors have retracted this article [1] because the article shows [2]. All authors agree to this retraction

In vitro and in vivo antiviral activity of monolaurin against Seneca Valley virus

IntroductionSurveillance of the Seneca Valley virus (SVV) shows a disproportionately higher incidence on Chinese pig farms. Currently, there are no vaccines or drugs to treat SVV infection effectively and effective treatment options are urgently needed.MethodsIn this study, we evaluated the antiviral activity of the following medium-chain fatty acids (MCFAs) or triglycerides (MCTs) against SVV: caprylic acid, caprylic monoglyceride, capric monoglyceride, and monolaurin.ResultsIn vitro experiments showed that monolaurin inhibited viral replication by up to 80%, while in vivo studies showed that monolaurin reduced clinical manifestations, viral load, and organ damage in SVV-infected piglets. Monolaurin significantly reduced the release of inflammatory cytokines and promoted the release of interferon-γ, which enhanced the viral clearance activity of this type of MCFA.DiscussionTherefore, monolaurin is a potentially effective candidate for the treatment of SVV infection in pigs

Measurement of differential cross sections for top quark pair production using the lepton plus jets final state in proton-proton collisions at 13 TeV

National Science Foundation (U.S.