Abstract
Consider the nonstationary Navier–Stokes equations in Ω × (0, T), where Ω is a general unbounded domain with non-compact boundary in R 3. We prove the regularity of suitable weak solutions for large |x|. It should be noted that our result also holds near the boundary. Our result extends the previous ones by Caffarelli–Kohn–Nirenberg in R 3 and Sohr-von Wahl in exterior domains to general domains.
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Suzuki, T. On partial regularity of suitable weak solutions to the Navier–Stokes equations in unbounded domains. manuscripta math. 125, 471–493 (2008). https://doi.org/10.1007/s00229-007-0163-6
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DOI: https://doi.org/10.1007/s00229-007-0163-6