Related papers: Existence theorems for regular solutions to the Ca…
In this paper, we establish global strong solutions for arbitrarily large initial data to the 2D and 3D compressible Navier-Stokes-Korteweg system, also referred to as the quantum Navier-Stokes equations, originally derived by Dunn and…
In 2016, Seregin and \u{S}ver\'ak, conceived a notion of global in time solution (as well as proving existence of them) to the three dimensional Navier-Stokes equation with $L_3$ solenoidal initial data called 'global $L_3$ solutions'. A…
Consider the equations of Navier-Stokes in $\R^3$ in the rotational setting, i.e. with Coriolis force. It is shown that this set of equations admits a unique, global mild solution provided the initial data is small with respect to the norm…
This paper concerns the Cauchy problem of the barotropic compressible Navier-Stokes equations on the whole two-dimensional space with vacuum as far field density. In particular, the initial density can have compact support. When the shear…
We prove that if $u$ is a suitable weak solution to the three dimensional Navier-Stokes equations from the space $L_{\infty}(0,T;\dot{B}_{\infty,\infty}^{-1})$, then all scaled energy quantities of $u$ are bounded. As a consequence, it is…
In this paper, we discuss the existence of local strong solutions for the multivalued version of three-dimensional nonstationary Navier-Stokes equation in Banach spaces. Also, we considered a more general inclusion problem and studied the…
We utilize undetermined coefficient method and an iterative method to construct the series solutions of the 3D Cauchy problem for a class of incompressible Navier-Stokes and Euler Equations. Then we can turn the Navier-Stokes Equations…
Motivated by applications to vortex rings, we study the Cauchy problem for the three-dimensional axisymmetric Navier-Stokes equations without swirl, using scale invariant function spaces. If the axisymmetric vorticity is integrable with…
The Navier-Stokes motions in a box with periodic boundary conditions are considered. First the existence of global regular two-dimensional solutions is proved. The solutions are such that continuous with respect to time norms are controlled…
Non-smooth Leray-Hopf solutions of the Navier-Stokes equation are constructed. The construction occurs in a finite periodic cube T3. Entropy production maximizing solutions with turbulent initial data are selected. The proof of finite time…
In this paper, we study the local existence and uniqueness of strong solutions for Cauchy problem of three-dimensional inhomogeneous incompressible Navier-Stokes-Vlasov equations, which are influenced by Young-Pil Choi, Bongsuk Kwon [London…
The micropolar equations are a useful generalization of the classical Navier-Stokes model for fluids with micro-structure. We prove the existence of global and strong solutions to these equations in cylindrical domains in $\mathbb{R}^3$. We…
We examine the so-called micropolar equations in three dimensional cylindrical domains under Navier boundary conditions. These equations form a generalization of the ordinary incompressible Navier-Stokes model, taking the structure of the…
This paper is concerned with the Cauchy problem of Navier-Stokes equations for compressible viscous heat-conductive fluids with far-field vacuum at infinity in $\R^3$. For less regular data and weaker compatibility condition than those…
We study the nonhomogeneous boundary value problem for the Navier--Stokes equations of steady motion of a viscous incompressible fluid in a three--dimensional exterior domain with multiply connected boundary. We prove that this problem has…
We consider the Navier-Stokes system describing the time evolution of a compressible barotropic fluid confined to a bounded spatial domain in the 3-D physical space, supplemented with the Navier's slip boundary conditions. It is shown that…
In this paper, we study existence times of strong solutions of the three-dimensional Navier-Stokes equations in time-varying analytic Gevrey classes based on Sobolev spaces $H^s, s> \frac{1}{2}$. This complements the seminal work of Foias…
In my PhD thesis I show the existence of global-in-time weak solutions for a Navier-Stokes fluid interacting with a linearly elastic shell of Koiter type. This is achieved by the introduction of a new method for showing the compactness of…
The problem of describing the behavior of the solutions to the Navier-Stokes equations in three space dimensions has always been borderline. From one side, due to the viscosity term, smooth data seem to produce solutions with an everlasting…
We consider the Cauchy problem for incompressible Navier-Stokes equations $u_t+u\nabla_xu-\Delta u+\nabla p=0, div u=0 in R^d \times R^+$ with initial data $a\in L^d(R^d)$, and study in some detail the smoothing effect of the equation. We…