arXiv subjects

Tarek Zoechling

Publications and source records attributed to Tarek Zoechling.

2 recordsLinked to original sources

arXiv2026

Local smooth solutions of the free-boundary compressible primitive equations with physical vacuum

Local existence and uniqueness of smooth solutions are established for the three-dimensional compressible primitive equations with constant viscosity and a physical vacuum free boundary. We employ a Nash-Moser approach to address two distinct derivative losses, one arising from the free boundary geometry in the transformed viscosity and the other from the diagnostic reconstruction of the vertical velocity. We handle the first through Alinhac's good velocity unknown and the second through a modified height. Combining these two corrections with weighted energy estimates adapted to the vacuum degeneracy yields the tame estimates required for the iteration.

math.AP↗

arXiv2026

Global well-posedness of the primitive equations with stochastic wind-driven boundary conditions

Consider the three-dimensional primitive equations subject to Neumann wind stress driven by finitely many Brownian motions. For arbitrary smooth spatial wind profiles, global pathwise existence and uniqueness without assuming a vertical derivative of the initial datum is proved, extending the local theory of Binz, Hieber, Hussein, and Saal: The primitive equations with stochastic wind driven boundary conditions (J. Math. Pures Appl. (9) (2024), 76--101) for this class of data and wind profiles. The proof combines a local maximal $\rL^2$ regularity construction with weighted estimates for the boundary stochastic convolution.

math.AP↗