Related papers: Low regularity solutions for the surface quasi-geo…
We provide the first proof of local well-posedness for the two-dimensional gravity water wave equations with spatially quasi-periodic initial conditions. We represent the solution using holomorphic coordinates, which are equivalent to a…
We show the existence of non-unique stationary weak solutions for forced surface quasi-geostrophic (SQG) equation via a convex integration scheme. The scheme is implemented for the sum-difference system of two distinct solutions. Through…
We provide a proof of global existence of solutions to quasilinear wave equations satisfying the null condition in certain exterior domains. In particular, our proof does not require estimation of the fundamental solution for the free wave…
The three-dimensional quasi-geostrophic equation is considered over a cylindrical domain with a multiply connected horizontal cross-section. Homogeneous Neumann boundary conditions, tantamount to homogeneous density fields, are imposed on…
We construct solutions in $\mathbb{R}^2$ with finite energy of the surface quasi-geostrophic equations (SQG) that initially are in $C^k$ ($k\geq 2$) but that are not in $C^{k}$ for $t>0$. We prove a similar result also for $H^{s}$ in the…
We study the temporal fluctuations of the flux of surface potential energy in Surface Quasi-Geostrophic (SQG) turbulence. By means of high-resolution, direct numerical simulations of the SQG model in the regime of forced and dissipated…
In this paper, we prove global well-posedness for low regularity data for the one dimensional quintic defocusing nonlinear Schr\"odinger equation. We show that a unique solution exists for $u_{0} \in H^{s}(\mathbf{R})$, $s > {8/29}$. This…
We consider surface quasi-geostrophic equation with dispersive forcing and critical dissipation. We prove global existence of smooth solutions given sufficiently smooth initial data. This is done using a maximum principle for the solutions…
We establish the small data solvability of suitable quasilinear wave and Klein-Gordon equations in high regularity spaces on a geometric class of spacetimes including asymptotically de Sitter spaces. We obtain our results by proving the…
The quasigeostrophic model is a simplified geophysical fluid model at asymptotically high rotation rate or at small Rossby number. We consider the quasigeostrophic equation with dissipation under random forcing in bounded domains. We show…
A result of Gevrey regularity is ascertained for a semigroup which models a fluid-structure interaction problem. In this model, the fluid evolves in a piecewise smooth or convex geometry $\mathcal{O}$. On a portion of the boundary, a fourth…
In this paper we construct a large class of non-trivial (non-radial) self-similar solutions of the generalized surface quasi-geostrophic equation (gSQG). To the best of our knowledge, this is the first rigorous construction of any…
The Cauchy problem for the Maxwell-Klein-Gordon equations in Lorenz gauge in two and three space dimensions is locally well-posed for low regularity data without finite energy. The result relies on the null structure for the main bilinear…
For the short pulse initial data with a first order outgoing constraint condition and optimal orders of smallness, we establish the global existence of smooth solutions to 2D quasilinear wave equations with higher order null conditions.…
We study the representation of solutions of the three-dimensional quasigeostrophic (QG) equations using Galerkin series with standard vertical modes, with particular attention to the incorporation of active surface buoyancy dynamics. We…
We consider in this article the system of (pure) gravity water waves in any dimension and in fluid domains with general bottoms. The unique solvability of the problem was established by Alazard-Burq-Zuily [Invent. Math, 198 (2014), no. 1,…
We consider the Maxwell-Klein-Gordon equation in 2D in the Coulomb gauge. We establish local well-posedness for $s=\frac 14+\epsilon$ for data for the spatial part of the gauge potentials and for $s=\frac 58+\epsilon$ for the solution…
We consider the forced surface quasi-geostrophic equation with supercritical dissipation. We show that linear instability for steady state solutions leads to their nonlinear instability. When the dissipation is given by a fractional…
We study spherically symmetric configurations of the quadratic $f(R)$ gravity in the Einstein frame. In case of a purely gravitational system, we have determined the global qualitative behavior of the metric and the scalaron field for all…
We develop, in the context of general relativity, the notion of a geoid -- a surface of constant "gravitational potential". In particular, we show how this idea naturally emerges as a specific choice of a previously proposed, more general…