Related papers: Sharp nonuniqueness for the forced 2D Navier-Stoke…
We prove non-uniqueness for a class of weak solutions to the Navier-Stokes equations which have bounded kinetic energy, integrable vorticity, and are smooth outside a fractal set of singular times with Hausdorff dimension strictly less than…
A well-known unsolved problem (in the classical theory of fluid mechanics) is to identify a set of initial velocities, which may depend on the viscosity, the body forces and possibly the boundary of the fluid that will allow global in time…
This paper introduces a robust reformulation of the incompressible Navier-Stokes equations, establishing a foundational framework for designing efficient, structure-preserving algorithms that strictly conserve the original energy…
In this paper we prove the existence and uniqueness of strong solution of the incompressible Navier-Stokes equations with damping $\alpha (e^{\beta|u|^2}-1)u$.
In this paper we develop a new way to study the global existence and uniqueness for the Navier-Stokes equation (NS) and consider the initial data in a class of modulation spaces $E^s_{p,q}$ with exponentially decaying weights $(s<0, \…
For any divergence free initial data in $H^\frac12$, we prove the existence of infinitely many dissipative solutions to both the 3D Navier-Stokes and MHD equations, whose energy profiles are continuous and decreasing on $[0,\infty)$. If the…
Strong solutions of the non-stationary Navier-Stokes equations under non-linearized slip or leak boundary conditions are investigated. We show that the problems are formulated by a variational inequality of parabolic type, to which…
We study the regularity of the weak limit of a sequence of dissipative solutions to the Navier--Stokes equations when no assumptions is made on the behavior of the pressures.
We consider the singularity formation of strong solutions to the two-dimensional full compressible Navier-Stokes equations with zero heat conduction in a bounded domain. It is shown that for the initial density allowing vacuum, the strong…
In this article, a non linear family of spaces, based on the energy dissipation, is introduced. This family bridges an energy space (containing weak solutions to Navier-Stokes equation) to a critical space (invariant through the canonical…
We consider a full Navier-Stokes and $Q$-tensor system for incompressible liquid crystal flows of nematic type. In the two dimensional periodic case, we prove the existence and uniqueness of global strong solutions that are uniformly…
The paper is concerned with the existence and uniqueness of a strong solution to a two-dimensional backward stochastic Navier-Stokes equation with nonlinear forcing, driven by a Brownian motion. We use the spectral approximation and the…
The aim of this paper is threefold. Firstly, we prove the existence and the uniqueness of a global strong (in both the probabilistic and the PDE senses) $\mathrm{H}^{1}_2$-valued solution to the 2D stochastic Navier-Stokes equations (SNSEs)…
The present paper deals with existence and uniqueness of global mild solutions for the 2D Navier-Stokes equations with impulses. Using the framework of nonautonomous dynamical systems, we extend previous results considering the 2D…
We study global well-posedness of strong solutions for the nonhomogeneous Navier-Stokes equations with density-dependent viscosity and initial density allowing vanish in $\mathbb{R}^2$. Applying a logarithmic interpolation inequality and…
This paper studies two hybrid discontinuous Galerkin (HDG) discretizations for the velocity-density formulation of the compressible Stokes equations with respect to several desired structural properties, namely provable convergence, the…
We establish a DMV-strong uniqueness result for the compressible Navier-Stokes system with potential temperature transport. The concept of generalized, the so-called dissipative measure-valued (DMV), solutions was proposed in [7], where…
The object of the present paper is to show the existence and the uniqueness of a reproductive strong solution of the Navier-Stokes equations, i.e. the solution $\boldsymbol{u} $ belongs to $\text{}\mathbf{L}% ^{\infty}(0,T;V) \cap…
In this paper we consider the r\^ole that numerical computations -- in particular Galerkin approximations -- can play in problems modelled by the 3d Navier-Stokes equations, for which no rigorous proof of the existence of unique solutions…
We establish new non-uniqueness results for the forced inviscid surface quasi-geostrophic equation, via an alternating formulation of convex integration techniques. Our results imply non-uniquenesss in the class of weak solutions with…