Related papers: Global weak solutions for SQG in bounded domains

We consider a two-dimensional MHD model describing the evolution of viscous, compressible and electrically conducting fluids under the action of vertical magnetic field without resistivity. Existence of global weak solutions is established…

We obtain a global weighted $L^p$ estimate for the gradient of the weak solutions to divergence form elliptic equations with measurable coefficients in a nonsmooth bounded domain. The coefficients are assumed to be merely measurable in one…

Global well-posedness of the initial-boundary value problem for the stochastic Kuramoto-Sivashinsky equation in a bounded domain $D$ with a multiplicative noise is studied. It is shown that under suitable sufficient conditions, for any…

We are interested in nonlocal Eikonal Equations arising in the study of the dynamics of dislocations lines in crystals. For these nonlocal but also non monotone equations, only the existence and uniqueness of Lipschitz and local-in-time…

In this paper, we revisit the patch solutions for a class of inviscid whole-space active scalar equations that interpolate between the 2D Euler equation and the $\alpha$-SQG equation. Compared with the 2D Euler equation in vorticity form,…

In this paper we show that after suitable data randomization there exists a large set of super-critical periodic initial data, in $H^{-\alpha}({\mathbb T}^d)$ for some $\alpha(d) > 0$, for both 2d and 3d Navier-Stokes equations for which…

We establish local boundedness for solutions to fractional porous medium-type equations in the fast diffusion regime, under optimal tail assumptions.

We study the existence of weak solutions to the $p$-Navier-Stokes equations with a symmetric $p$-Laplacian on bounded domains. We construct a particular Schauder basis in $W_0^{1,p}(\Omega)$ with divergence free constraint and prove…

We consider a nonlinear, spatially-nonlocal initial value problem in one space dimension on $\mathbb{R}$ that describes the motion of surface quasi-geostrophic (SQG) fronts. We prove that the initial value problem has a unique local smooth…

Global uniform boundedness of solutions to 3D viscous Primitive equations in a bounded cylindrical domain with physical boundary condition is proved in space $H^m$ for any $m\geqslant2$. A bounded absorbing set for the solutions in $H^m$ is…

We establish new sufficient conditions for the existence of weak Besicovitch quasiperiodic solutions for natural Lagrangian system on Riemannian manifold with time-quasiperiodic force function

We establish the well/ill-posedness theories for the inviscid $\alpha$-surface quasi-geostrophic ($\alpha$-SQG) equations in H\"older spaces, where $\alpha = 0$ and $\alpha = 1$ correspond to the two-dimensional Euler equation in the…

We prove the existence and uniqueness of global solutions to the semilinear stochastic heat equation on an unbounded spatial domain with forcing terms that grow superlinearly and satisfy an Osgood condition $\int 1/|f(u)|du = +\infty$ along…

This paper deals with the Weak Inverse Galois Problem which, for a given field $k$, states that, for every finite group $G$, there exists a finite separable extension $L/k$ such that ${\rm{Aut}}(L/k)=G$. One of its goals is to explain how…

We prove that the solutions of the defocusing cubic wave equation on T2 exist globally in time in Hs(T2) for s > 2/5 by contradiction. Assuming that one of the maximal times of existence is finite, we prove that the Sobolev norm of each of…

In this paper, we consider the global solutions to a generalized 2D Boussinesq equation \begin{align*} \left \{\begin{aligned} & \partial_{t} \omega + u\cdot \nabla \omega + \nu \Lambda^{\alpha} \omega = \theta_{x_{1}} , \quad \\ & u =…

In this paper, we show existence of white noise solutions for weak formulations of modified Surface Quasi-Geostrophic (mSQG) equations. Based on previous results (\cite{FS}) on white noise solutions for mSQG equations on the torus…

This paper studies the existence and asymptotic behavior of global weak solutions for a thin film equation with insoluble surfactant under the influence of gravitational, capillary and van der Waals forces. We prove the existence of global…

This paper is concerned with an initial-boundary value problem of the two-dimensional inhomogeneous primitive equations with density-dependent viscosity. The global well-posedness of strong solutions is established, provided the initial…

In this work we consider the problem of global existence of small regular solutions to a type nonlinear wave-Klein-Gordon system with semi-linear interactions in two spatial dimension. We develop some new techniques on both wave equations…