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By the special solutions we can choose spherically symmetric solutions. Let $v$, $\\varrho$ be a~solution to our problem. Then we are looking for differences $u=v-v_s$, $\\eta=\\varrho-\\varrho_s$. We prove existence of $u$, $\\eta$ such that $u,\\eta\\in L_\\infty(kT,(k+1)T;H^2(\\Omega))$, $u_t,\\eta_t\\in L_\\infty(kT,(k+1)T;H"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1508.06127","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-25T12:30:28Z","cross_cats_sorted":[],"title_canon_sha256":"807b0b88800baa43655655f21035bb23da606f903e77d30fb765d165e5e44475","abstract_canon_sha256":"83bf570d7ea9fc50468763156f1d470c1e1c28be4e821e0241f05a38ba918524"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:46.742725Z","signature_b64":"H7kaS6tIVQ39y+ihts0CSRHUUDjzK48j1YD7AMuXayh9KpvnQU5l89F6BwfHSHL1O5s57+BDYzFGjZp9ZEMkDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6013b3ca4d46f8d7535aef33e93da3b69d6bf2bc9e828d294afd025ba2de0cc","last_reissued_at":"2026-05-18T01:34:46.742097Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:46.742097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global regular motions for compressible barotropic viscous fluids. 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