Related papers: Well-posedness for the Navier-Stokes equations in …
We shall prove dispersive and smoothing estimates for Bochner type laplacians on some non-compact Riemannian manifolds with negative Ricci curvature, in particular on hyperbolic spaces. These estimates will be used to prove Fujita-Kato type…
We investigate in the present paper the Navier-Stokes equations on quantum Euclidean spaces $\mathbb{R}^d_{\theta}$ with $\theta$ being a $d\times d$ antisymmetric matrix, which is a standard example of non-compact noncommutative manifolds.…
In this paper we consider the incompressible inhomogeneous Navier-Stokes equations in the whole space with dimension $n\geq 3$. We present local and global well-posedness results in a new framework for inhomogeneous fluids, namely…
We study the Cauchy problem in $n$-dimensional space for the system of Navier-Stokes equations in critical mixed-norm Lebesgue spaces. Local well-posedness and global well-posedness of solutions are established in the class of critical…
We investigate sufficient H\"older continuity conditions on Leray-Hopf (weak) solutions to the in unsteady Navier-Stokes equations in three dimensions guaranteeing energy conservation. Our focus is on the half-space case with homogeneous…
In this paper, we study the existence, uniqueness and asymptotic behaviour of almost periodic and asymptotically almost periodic mild solutions to the incompressible Navier-Stokes equations on $d$-dimensional non-compact manifold…
We study mild solutions to the Navier-Stokes equation on the $n$-dimensional hyperbolic space $\mathbb{H}^n$, $n \geq 2$. We use dispersive and smoothing estimates proved by Pierfelice on a class of complete Riemannian manifolds to extend…
We demonstrate that the three dimensional incompressible magneto-hydrodynamics (MHD) system is ill-posed due to the discontinuity of weak solutions in a wide range of spaces. Specifically, we construct initial data which has finite energy…
In this paper, we mainly study the Cauchy problem for the full compressible Navier-Stokes equations in Sobolev spaces. We establish the global well-posedness of the equations with small initial data by using Friedrich's method and…
The present paper is dedicated to the global well-posedness for the 3D inhomogeneous incompressible Navier-Stokes equations, in critical Besov spaces without smallness assumption on the variation of the density. We aim at extending the work…
We study the incompressible stationary Navier-Stokes equations in the upper-half plane with homogeneous Dirichlet boundary condition and non-zero external forcing terms. Existence of weak solutions is proved under a suitable condition on…
The initial value problem of the incompressible Navier-Stokes equations with non-zero forces in $L^{n,\infty}(\mathbb{R}^n)$ is investigated. Even though the Stokes semigroup is not strongly continuous on $L^{n,\infty}(\mathbb{R}^n)$, with…
In this paper, we investigate the well-posedness theory and exponential stability for the inhomogeneous incompressible Navier-Stokes equation with only horizontal dissipative structure. Due to the lack of the vertical dissipative term and…
We discuss the appearance of spatial asymptotic expansions of solutions of the Navier-Stokes equation on $\mathbb{R}^n$. In particular, we prove that the Navier-Stokes equation is locally well-posed in a class of weighted Sobolev and…
In this paper, the local well-posedness of strong solutions to the Cauchy problem of the isentropic compressible Navier-Stokes equations is proved with the initial date being allowed to have vacuum. The main contribution of this paper is…
In this paper, authors show the ill-posedness of 3D incompressible Navier-Stokes equations in the critical Triebel-Lizorkin spaces $ \dot{F}^{-1,q}_{\infty} (\mathbb{R}^3) $ for any $ q>2 $ in the sense that arbitrarily small initial data…
This paper concerns the existence of global weak solutions \`a la Leray for compressible Navier-Stokes equations with a pressure law that depends on the density and on time and space variables $t$ and $x$. The assumptions on the pressure…
We establish the existence and uniqueness of local strong solutions to the Navier-Stokes equations with arbitrary initial data and external forces in the homogeneous Besov-Morrey space. The local solutions can be extended globally in time…
In this work, we proved the existence of a unique global mild solution of the d-dimensional incompressible Navier-Stokes equations, for small initial data in Besov type spaces based on mixed-Lebesgue spaces; namely, mixed-norm…
The incompressible Navier-Stokes equations are re-formulated to involve an arbitrary time dilation; and in this manner, the modified Navier-Stokes equations are obtained which have some penalization terms in the right hand side. Then, the…