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For the compressible Navier–Stokes equations with viscosity and heat conductivity coefficients possibly depending on the density or temperature, several blowup criteria are given to the local-in-time strong solutions. The proof is based on energy methods together with elliptic and parabolic estimates adopted to the present situation.

Auditory information is initially processed in the cochlear nuclei before being relayed to the brain. The cochlear nuclei are subdivided into dorsal, anterior ventral, and posterior ventral domains, each containing several subtypes of neurons that are thought to play discrete roles in the processing of sound. However, the ontogeny of these neurons is poorly understood, and this gap in knowledge hampers efforts to understand the basic neural circuitry of this nucleus. Here, we reveal that Bhlhb5 is expressed in both excitatory (unipolar brush cells) and inhibitory neurons (cartwheel cells) of the DCN during development. To gain genetic access to Bhlhb5-expressing neurons in the DCN, we generated a Bhlhb5::flpo knockin allele. Using an intersectional genetic strategy, we labeled cartwheel cells, thereby providing proof of concept that subpopulations of Bhlhb5-expressing neurons can be genetically targeted. Moreover, fate-mapping experiments using this allele revealed that Bhlhb5 is required for the proper development of the DCN, since mice lacking Bhlhb5 showed a dramatically diminished number of neurons, including unipolar brush and cartwheel cells. Intriguingly, the Bhlhb5::flpo allele also genetically labels numerous other regions of the nervous system that process sensory input, including the dorsal horn, the retina, and the nucleus of the lateral olfactory tract, hinting at a more general role for Bhlhb5 in the development of neurons that mediate sensory integration.

We prove global-in-time existence of regular solution to the initial value problem of a 2-D Kazhikhov–Smagulov type model for incompressible nonhomogeneous fluids with mass diffusion.

Primary afferents are known to be inhibited by kappa opioid receptor (KOR) signaling. However, the specific types of somatosensory neurons that express KOR remain unclear. Here, using a newly developed KOR-cre knockin allele, viral tracing, single-cell RT-PCR, and ex vivo recordings, we show that KOR is expressed in several populations of primary afferents: a subset of peptidergic sensory neurons, as well as low-threshold mechanoreceptors that form lanceolate or circumferential endings around hair follicles. We find that KOR acts centrally to inhibit excitatory neurotransmission from KOR-cre afferents in laminae I and III, and this effect is likely due to KOR-mediated inhibition of Ca2+ influx, which we observed in sensory neurons from both mouse and human. In the periphery, KOR signaling inhibits neurogenic inflammation and nociceptor sensitization by inflammatory mediators. Finally, peripherally restricted KOR agonists selectively reduce pain and itch behaviors, as well as mechanical hypersensitivity associated with a surgical incision. These experiments provide a rationale for the use of peripherally restricted KOR agonists for therapeutic treatment.

Peripherally-restricted kappa opioid receptor (KOR) agonists are emerging as a novel treatment for pain and itch conditions and have shown efficacy in several recent clinical trials. One primary site of action is thought to be at KORs on primary afferent nerves that innervate the body. Yet, the subtypes of primary afferent somatosensory neurons that express the kappa opioid receptor remain undefined. Using a newly developed KOR-cre knockin allele, viral tracing, and single-cell RT-PCR we discovered that that KOR is expressed in a specific subset of peptidergic afferents. This subset targeted multiple tissue types and expressed higher levels of transcripts known to be involved in neurogenic inflammation. Consistent with this, peripherally-restricted KOR agonists inhibited behavioral responses to chemical pain and itch stimuli, but not acute heat stimuli, and also decreased mechanical hypersensitivity following an incision injury. Unexpectedly, we also found that KOR is expressed in subsets of primary afferents that form lanceolate or circumferential endings around hair follicles, suggesting an unappreciated role for KOR signaling in the modulation of low-threshold mechanosensation. At a functional level, genetically-labeled afferents showed inhibition of voltage-gated calcium current in response to kappa agonists, and optogenetic experiments revealed that dynorphin inhibited evoked-EPSCs from the central terminals of KOR-expressing afferents. These experiments provide key insight for the rationale use of peripherally-restricted KOR agonists for the modulation of inflammatory pain, itch, and potentially mechanical allodynia.