HIGHER-ORDER REGULARITY AND CONTINUOUS DATA ASSIMILATION FOR THE VELOCITY-VORTICITY MODEL OF THE g-NAVIER-STOKES EQUATIONS

Kazar Ö., KAYA M.

Palestine Journal of Mathematics, cilt.14, sa.3, ss.1245-1261, 2025 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 3
  • Basım Tarihi: 2025
  • Dergi Adı: Palestine Journal of Mathematics
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.1245-1261
  • Anahtar Kelimeler: Continuous data assimilation, Higher-order regularity, Velocity-Vorticity model
  • Gazi Üniversitesi Adresli: Evet

Özet

In this paper, we aim to improve the known results of the weak and strong solutions of the two-dimensional velocity-vorticity model of the g-Navier Stokes equations (gNSEs). Using energy estimation methods, we obtain the higher-order regularity of the solution of this model. Then we introduce an algorithm for continuous data assimilation for the velocity–vorticity model of the g-NSEs in the two-dimensional case. We give conditions on the spatial resolution of the observed data which are sufficient to show that the solution of the algorithm approaches, at an exponential rate, the unique exact unknown solution of this model.