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This paper focuses on establishing the existence of smooth solutions for the incompressible Landau-Lifshitz-Gilbert equation with Dzyaloshinskii-Moriya (DM) interaction and V flow in two-dimensional domains, including the torus and Euclidean space. The primary objective is to establish global existence results by investigating the conditions under which a smooth solution exists for all time, provided that the L² norm of the initial magnetization gradient is sufficiently small. Rigorous mathematical proofs for these global existence results are provided by combining analytical techniques and energy estimates. These findings enhance our understanding of solution behavior and regularity in the Landau-Lifshitz-Gilbert equation with DM interaction, shedding light on its dynamics in different spatial domains. [ABSTRACT FROM AUTHOR]

In this paper, we investigate nonhomogeneous incompressible Navier–Stokes–Landau–Lifshitz system in two‐dimensional (2‐D). This system consists of Navier–Stokes equations coupled with Landau–Lifshitz–Gilbert equation, an evolutionary equation for the magnetization vector. We establish a blowup criterion for the 2‐D incompressible Navier–Stokes–Landau–Lifshitz system with finite positive initial density. [ABSTRACT FROM AUTHOR]

In this paper, we prove that any smooth solutions of quantum hydrodynamic model which satisfies suitable conditions will blow up in finite time in half space. This model can be considered as the compressible Euler equation with quantum potential. The main ideal is based on the construction of energy inequality. [ABSTRACT FROM AUTHOR]

Mitochondrial permeability transition (MPT) pores have recently been implicated as a potential mediator of myocardial ischemic injury. Nitric oxide (NO) donors induce a poweful late phase of cardioprotection against ischemia-reperfusion injury; however, the cellular mechanisms involved are poorly understood. The role of MPT pores as a target of cardioprotective signaling pathways activated by NO has never been explored in detail. Thus mice were administered the NO donor diethylenetriamine (DETA)/NO (4 doses of 0.1 mg/kg iv each) 24 h before 30 min of coronary artery occlusion followed by 24 h of repeffusion. Infarct size was significantly reduced in DETA/NO-treated ngne (30 ± 2% of risk region in treated mice vs 50 ± 2% in control mice; P < 0.05), which demonstrates powerful cardioprotection. To examine the role of MPT pores, mice were administered atractyloside (Atr; 25 mg/kg iv), which induces adenine nucleotide translocase-dependent MPT, 20 min before ischemia. Atr blocked the infarct-sparing effects of DETA/NO (infarct size, 58 ± 1 vs, 30 ± 2% of risk region in DETA/NO; P < 0.05), whereas Atr alone had no effect. Mitochondria isolated from DETA/NO-treated mice exhibited increased resistance to Ca2+-thdueed swelling by 20 μmol/l CaCl2 or by the higher concentration of 200 μmol/l, which suggests that cardioprotection involves decreased propensity for MPT. Preincubation of mitochondria from control hearts with 30 nmol/l of the pore inhibitor cyclosporin A prevented swelling by 200 μmol/l CaCl2, thereby confirming that Ca2+ induces mitochondrial swelling via MPT. In accordance with the effects on infarct size, administration of Atr to the mice significantly abrogated DETA/NO-induced protection against Ca2+-induced mitochondrial swelling. These phenotypic alterations were associated with an increase in the antiapoptotic protein Bcl-2, which suggests that the underlying mechanisms may involve inhibition of cell death by Bcl-2. These data suggest that a critical process during NO donor-induced cardioprotection is to prevent MPT pore opening potentially via targeting of the adenine nucleotide translocator. [ABSTRACT FROM AUTHOR]