{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T11:17:27Z","timestamp":1762859847095,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T00:00:00Z","timestamp":1762300800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Imam Mohammad ibn Saud Islamic University","award":["IMSIU-DDRSP2503"],"award-info":[{"award-number":["IMSIU-DDRSP2503"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We study the three-dimensional modified critical homogeneous convective Brinkman\u2013Forchheimer equations. Local existence and uniqueness are obtained via the Fixed Point Theorem, and under the assumption of finite maximal existence time, we establish blow-up criteria in Sobolev\u2013Gevrey spaces. The model preserves Euclidean invariances (translations and rotations) and, when \u03b1=0, the critical scaling symmetry of the 3D Navier-Stokes system. The blow-up thresholds are shown to depend mainly on the Gevrey structure rather than on any loss of symmetry.<\/jats:p>","DOI":"10.3390\/sym17111877","type":"journal-article","created":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T13:19:29Z","timestamp":1762348769000},"page":"1877","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Symmetry and Blow-Up for 3D Modified CBF Equations in Sobolev\u2013Gevrey Spaces"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7604-0955","authenticated-orcid":false,"given":"Lotfi","family":"Jlali","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6215-5305","authenticated-orcid":false,"given":"Ibtehal","family":"Alazman","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"7141","DOI":"10.1016\/j.jde.2017.08.001","article-title":"Energy equality for the 3D critical convective Brinkman-Forchheimer equations","volume":"263","author":"Hajduk","year":"2017","journal-title":"J. Differ. Equ."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1292","DOI":"10.1088\/0951-7715\/29\/4\/1292","article-title":"Continuous data assimilation for the three-dimensional Brinkman-Forchheimer-extended Darcay model","volume":"29","author":"Markowich","year":"2016","journal-title":"Nonlinearity"},{"key":"ref_3","unstructured":"Ladyzhenskaya, O.A. (1969). The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach."},{"key":"ref_4","unstructured":"Temam, R. (1984). Navier-Stokes Equations, Theory and Numerical Analysis, North-Holland."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"590","DOI":"10.1515\/math-2022-0050","article-title":"Global weak solution of 3D-NSE with exponential damping","volume":"20","author":"Benameur","year":"2022","journal-title":"Open Math."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1016\/j.jmaa.2008.01.041","article-title":"Weak and Strong solutions for the incompressible Navier-Stokes euations with daping","volume":"343","author":"Cai","year":"2008","journal-title":"J. Math. Anal. Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"20240013","DOI":"10.1515\/dema-2024-0013","article-title":"Long time decay of incompressible convective Brinkman-Forchheimer equation in L2(R3)","volume":"57","author":"Jlali","year":"2024","journal-title":"Demonstr. Math."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Jlali, L. (Discret. Contin. Dyn.-Syst. S, 2025). 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Theory Methods Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"805","DOI":"10.1007\/s00021-016-0263-8","article-title":"On the blow-up criterion of 3D- NSE in Sobolev-Gevrey spaces","volume":"18","author":"Benameur","year":"2016","journal-title":"J. Math. Fluid Mech."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/11\/1877\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T11:12:53Z","timestamp":1762859573000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/11\/1877"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,5]]},"references-count":14,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["sym17111877"],"URL":"https:\/\/doi.org\/10.3390\/sym17111877","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,11,5]]}}}