  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.
