Related papers: Non-uniqueness of weak solutions to 2D generalized…

In this article, we study the non-uniqueness of weak solutions for the two-dimensional hyper-dissipative Navier-Stokes equations in the super-critical spaces $L_{t}^{\gamma}W_{x}^{s,p}$ when $\alpha\in[1,\frac{3}{2})$, and obtain the…

In this paper, we prove a sharp nonuniqueness result for the incompressible Navier-Stokes equations in the periodic setting. In any dimension $d \geq 2$ and given any $ p<2$, we show the nonuniqueness of weak solutions in the class $L^{p}_t…

In this paper, we prove a sharp and strong non-uniqueness for a class of weak solutions to the incompressible Navier-Stokes equations in $\R^3$. To be more precise, we exhibit the non-uniqueness result in a strong sense, that is, any weak…

We study the 3D hyperdissipative Navier-Stokes equations on the torus, where the viscosity exponent $\alpha$ can be larger than the Lions exponent $5/4$. It is well-known that, due to Lions [55], for any $L^2$ divergence-free initial data,…

In this paper we establish a sharp non-uniqueness result for stochastic $d$-dimensional ($d\geq2$) incompressible Navier-Stokes equations. First, for every divergence free initial condition in $L^2$ we show existence of infinite many global…

In this paper, we prove that weak solutions to the 2D viscous and resistive magnetohydrodynamic (MHD) equations are non-unique in $L^2_t L^p(\mathbb{R}^2) \cap L^1_t W^{1,p}(\mathbb{R}^2)$ for given any $1\le p<\infty$, showing the…

In this paper, we prove a sharp and strong non-uniqueness for a class of weak solutions to the three-dimensional magneto-hydrodynamic (MHD) system. More precisely, we show that any weak solution $(v,b)\in L^p_tL^{\infty}_x$ is non-unique in…

We prove the non-uniqueness of weak solutions to 3D hyper viscous and resistive MHD in the class $L^\gamma_tW^{s,p}_x$, where the exponents $(s,\gamma,p)$ lie in two supercritical regimes. The result reveals that the scaling-invariant…

We prove a sharp nonuniqueness result for the forced generalized SQG equation. First, this yields nonunique $\dot{H}^s$- energy solutions below the Miura-Ju class. In particular, this shows that the solutions constructed by Resnick and…

We study the forward self-similar solutions to the $2$D hypodissipative Navier-Stokes equation with fractional diffusion $(-\Delta)^\alpha$ for $\frac{1}{2}<\alpha<1$. We first show that for arbitrarily large $(1-2\alpha)$-homogeneous…

The weak solution to the Navier-Stokes equations in a bounded domain $D \subset \mathbb{R}^3$ with a smooth boundary is proved to be unique provided that it satisfies an additional requirement. This solution exists for all $t \geq 0$. In a…

In this paper we are concerned with the 2D incompressible Navier-Stokes equations driven by space-time white noise. We establish existence of infinitely many global-in-time probabilistically strong and analytically weak solutions $u$ for…

We are concerned with the three dimensional incompressible Navier--Stokes equations driven by an additive stochastic forcing of trace class. First, for every divergence free initial condition in $L^{2}$ we establish existence of infinitely…

We exhibit non-unique Leray solutions of the forced Navier-Stokes equations with hypodissipation in two dimensions. Unlike the solutions constructed in \cite{albritton2021non}, the solutions we construct live at a supercritical scaling, in…

This article studies the uniqueness of the weak solution of the incompressible Navier-Stokes Equations in the 3-dimensional case. Here, the investigation is provided using two different approaches. The first (the main) result is obtained…

In this paper, we consider the 2D incompressible Navier-Stokes equations on the torus. It is well known that for any $L^2$ divergence-free initial data, there exists a global smooth solution that is unique in the class of $C_t L^2$ weak…

We consider the Navier-Stokes equation on $\mathbb{H}^{2}(-a^{2})$, the two dimensional hyperbolic space with constant sectional curvature $-a^{2}$. We prove an ill-posedness result in the sense that the uniqueness of the Leray-Hopf weak…

In this paper, we consider the generalized Navier-Stokes equations with fritional dissipation $(-\Delta)^{\beta}$ with $\beta>\frac{1}{2}$. When $\beta\in(1,2)$, We prove that smooth solutions of the generalized Navier-Stokes equations are…

We show the existence of global weak solutions of the 3D Navier-Stokes equations with initial velocity in the weighted spaces L 2 w$\gamma$ , where w $\gamma$ (x) = (1 + |x|) --$\gamma$ and 0 < $\gamma$ $\le$ 2, using new energy controls.…

Here we investigate 3-dimensional Navier-Stokes Equations in the incompressible case with use of different approach and we prove the uniqueness of the weak solutions for the data from the space, which is dense in usual space of data.…