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.
We consider a 3D rotating Navier-Stokes equation with transport-stretching noise, posed between two horizontal plates, and study the joint limit of vanishing vertical viscosity and rapid rotation. Our driving noise depends only on the horizontal coordinates and its vertical component vanishes with the viscosity. Provid...
For any $\gamma \in \left[ {0,\frac{1}{3}} \right)$, we construct $\gamma$-H\"{o}lder-continuous martingale solutions to the two-dimensional stochastic incompressible Euler equations. These martingale solutions exhibit dissipative behavior and intermittency, thereby establishing the flexible part of the intermittent On...
We study a stochastic Navier--Stokes system in which the spatial modes of the transport noise evolve dynamically and are coupled to the resolved velocity. The model couples a Navier--Stokes stochastic PDE to an infinite family of linearized Navier-Stokes equations for the noise correlation modes. These latter equations...
A. Debussche, E. Mémin, Sébastien Moskowitz· 0 citations
We establish the local-in-time existence and uniqueness of monotone solutions to the two-dimensional nonstationary boundary-layer equations for a dilatant power-law fluid in a periodic half-space for $1<n<\frac{7}{3}$. Under Oleinik's monotonicity condition and suitable weighted Sobolev assumptions on the initial data...
We show that the Navier-Stokes equations on $\mathbb R^2\times\mathbb T$ are globally well posed for initial vorticities that are both helically symmetric and integrable. This class of data typically generates velocity fields of infinite kinetic energy, so this result is not covered by the classical finite-energy well-...
Francisco Gancedo, Antonio Hidalgo-Torn'e· 0 citations
We study a fully discrete approximation theory for the two-dimensional incompressible Euler equations on $\mathbb{T}^{2}$, in vorticity form, driven by Kraichnan-type transport noise and with $\mathbb{H}^{-1}(\mathbb{T}^2)$-valued initial vorticity. The main new ingredient is a finite-dimensional coercivity estimate fo...
Abhishek Chaudhary, U. Koley, A. Prohl· 0 citations
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