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Abstract. The expansion waves for the compressible Navier-Stokes equations have recently been shown to be nonlinear stable. The nonlinear stability results are called local stability or global stability depending on whether the H 1 −norm of the initial perturbation is small or not. Up to now, local stability results have been well established. However, for global stability, only partial results have been obtained. The main purpose of this paper is to study the global stability of rarefaction waves for the compressible Navier-Stokes equations. For this purpose, we introduce a positive parameter t 0 in the construction of smooth approximations of the rarefaction wave solutions for the compressible Euler equations so that the quantity = t 0 δ (δ denotes the strength of the rarefaction waves) is sufficiently large to control the growth induced by the nonlinearity of the system and the interaction of waves from different families. Then by using the energy method together with the continuation argument, we obtain some nonlinear stability results provided that the initial perturbation satisfies certain growth conditions as → +∞. Notice that the assumption that the quantity can be chosen to be sufficiently large implies that either the strength of the rarefaction waves is small or the rarefaction waves of different families are separated far enough initially.

Ginkgolide K, a natural platelet-activating factor receptor antagonist, was isolated from the leaves of Ginkgo biloba. However, little is known about its neuroprotective effect in ischemia-reperfusion (I/R)-induced cerebral injury. Hence, the present study was carried out to investigate the effect of ginkgolide K on neuroprotection and the potential mechanisms in the rat I/R model induced by middle cerebral artery occlusion (MCAO). The rats were pretreated with ginkgolide K 2, 4 and 8 mg/kg (i.v.) once a day for 5 days before MCAO. Neurological deficit score (NDS), brain water content, 2,3,5-triphenyltetrazolium chloride (TTC) staining and pathology of brain tissue, as well as indexes of oxidative stress [superoxide dismutase (SOD), malondialdehyde (MDA), nitric oxide (NO) and nitric oxide synthase (NOS)] were measured at 24 h after ischemia. The results indicated that pretreatment with ginkgolide K significantly diminished the volume of infarction and brain water content, and improved NDS. Moreover, ginkgolide K markedly reversed the level of MDA, NO, NOS and SOD to their normal state in serum or cerebral ischemic section. In addition, hematoxylin and eosin staining showed the neuronal injury was significantly improved after being pretreated with ginkgolide K. These findings demonstrate that ginkgolide K exhibits neuroprotective properties through its antioxidative action in MCAO rats.