Search Results

Now showing 1 - 2 of 2
  • Item
    Local Well-Posedness of Strong Solutions to the Three-Dimensional Compressible Primitive Equations
    (Berlin ; Heidelberg : Springer, 2021) Liu, Xin; Titi, Edriss S.
    This work is devoted to establishing the local-in-time well-posedness of strong solutions to the three-dimensional compressible primitive equations of atmospheric dynamics. It is shown that strong solutions exist, are unique, and depend continuously on the initial data, for a short time in two cases: with gravity but without vacuum, and with vacuum but without gravity. © 2021, The Author(s).
  • Item
    Well-posedness of Hibler's dynamical sea-ice model
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Liu, Xin; Thomas, Marita; Titi, Edriss
    This paper establishes the local-in-time well-posedness of solutions to an approximating system constructed by mildly regularizing the dynamical sea ice model of it W.D. Hibler, Journal of Physical Oceanography, 1979. Our choice of regularization has been carefully designed, prompted by physical considerations, to retain the original coupled hyperbolic-parabolic character of Hibler's model. Various regularized versions of this model have been used widely for the numerical simulation of the circulation and thickness of the Arctic ice cover. However, due to the singularity in the ice rheology, the notion of solutions to the original model is unclear. Instead, an approximating system, which captures current numerical study, is proposed. The well-posedness theory of such a system provides a first-step groundwork in both numerical study and future analytical study.