On the weak solution for the regularized Bénard problem with damping

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ATMACA A., Kaya M.

Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, cilt.74, sa.2, ss.219-227, 2025 (ESCI)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 74 Sayı: 2
• Basım Tarihi: 2025
• Doi Numarası: 10.31801/cfsuasmas.1551018
• Dergi Adı: Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics
• Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
• Sayfa Sayıları: ss.219-227
• Gazi Üniversitesi Adresli: Evet

Özet

In this paper, we examine the regularized B ́enard problem in porous media within three- dimensional case. We consider the regularized B ́enard problem with damping a|u|2β u. The results hold in the context of periodic boundary conditions. We prove the existence of weak solutions for any β ≥ 0 and establish uniqueness of the weak solution for any 5/4 ≤ β ≤ 2.