Observations of the $gamma$-ray emission around star clusters, isolated supernova remnants, and pulsar wind nebulae indicate that the cosmic-ray (CR) diffusion coefficient near acceleration sites can be suppressed by a large factor compared to the Galaxy average. We explore the effects of such local suppression of CR diffusion on galaxy evolution using simulations of isolated disk galaxies with regular and high gas fractions. Our results show that while CR propagation with constant diffusivity can make gaseous disks more stable by increasing the midplane pressure, large-scale CR pressure gradients cannot prevent local fragmentation when the disk is unstable. In contrast, when CR diffusivity is suppressed in star-forming regions, the accumulation of CRs in these regions results in strong local pressure gradients that prevent the formation of massive gaseous clumps. As a result, the distribution of dense gas and star formation changes qualitatively: a globally unstable gaseous disk does not violently fragment into massive star-forming clumps but maintains a regular grand-design spiral structure. This effect regulates star formation and disk structure and is qualitatively different from and complementary to the global role of CRs in vertical hydrostatic support of the gaseous disk and in driving galactic winds.
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