Related papers: Approximation of 2D Euler Equations by the Second-…
We consider the evolution of an incompressible two-dimensional perfect fluid as the boundary of its domain is deformed in a prescribed fashion. The flow is taken to be initially steady, and the boundary deformation is assumed to be slow…
In this paper, we investigate the uniform regularity of solutions to the 3-dimensional isentropic compressible Navier-Stokes system with free surfaces and study the corresponding asymptotic limits of such solutions to that of the…
We consider a flow of non-Newtonian heat conducting incompressible fluid in a bounded domain subjected to the homogeneous Dirichlet boundary condition for the velocity field and the spatially inhomogeneous Dirichlet boundary condition for…
The Navier-Stokes-Voigt model of viscoelastic incompressible fluid has been recently proposed as a regularization of the three-dimensional Navier-Stokes equations for the purpose of direct numerical simulations. Besides the kinematic…
We consider the zero viscosity limit of the incompressible Navier-Stokes equations with non-slip boundary condition in the half-space for the initial vorticity located away from the boundary. By using the vorticity formulation and…
Well-posedness for the two dimensional Euler system with given initial vorticity is known since the works of Judovi\v{c}. In this paper we show existence of solutions in the case where we allowed the fluid to enter in and exit from the…
We consider the interaction of a compressible fluid with a flexible plate in two space dimensions. The fluid is described by the Navier--Stokes equations in a domain that is changing in accordance with the motion of the structure. The…
We prove that if the local second-order structure function exponents in the inertial range remain positive uniformly in viscosity, then any spacetime $L^2$ weak limit of Leray--Hopf weak solutions of the Navier-Stokes equations on any…
In this paper, we study the well-posedeness at low regularity of a two-dimensional system obtained as a reduced model for micropolar fluid dynamics. At the mathematical level, the system presents a coupling between an Euler-type equation…
We consider the incompressible Euler or Navier-Stokes (NS) equations on a torus T^d in the functional setting of the Sobolev spaces H^n(T^d) of divergence free, zero mean vector fields on T^d, for n > d/2+1. We present a general theory of…
The present paper is motivated by recent mathematical work on the incompressible Euler and Navier-Stokes equations, partly having physically problematic results and unrealistic expectations. The Euler and Navier-Stokes equations are…
In this paper we investigate the inviscid limit $\nu \to 0$ for time-quasi-periodic solutions of the incompressible Navier-Stokes equations on the two-dimensional torus ${\mathbb T}^2$, with a small time-quasi-periodic external force. More…
In this paper, we study the Cauchy problem of a two-phase flow system consisting of the compressible isothermal Euler equations and the incompressible Navier-Stokes equations coupled through the drag force, which can be formally derived…
We obtain existence and conormal Sobolev regularity of strong solutions to the 3D compressible isentropic Navier-Stokes system on the half-space with a Navier boundary condition, over a time that is uniform with respect to the viscosity…
The ideal incompressible fluid in two dimensions (Euler fluid) evolves at relaxation from turbulent states to highly coherent states of flow. For the case of double spatial periodicity and zero total vorticity it is known that the…
In this paper, we study the two-dimensional steady compactly supported incompressible Euler equations with free boundaries. We consider flows with constant vorticity that are perturbations of annular equilibria, in contrast to the laminar…
We consider the complete Euler system describing the time evolution of a general inviscid compressible fluid. We introduce a new concept of measure-valued solution based on the total energy balance and entropy inequality for the physical…
The quasi-neutral limit of the Navier-Stokes-Poisson system modeling a viscous plasma with vanishing viscosity coefficients in the half-space $\mathbb{R}^{3}_{+}$ is rigorously proved under a Navier-slip boundary condition for velocity and…
The purpose of this note is to give a complete proof of a $C^{0,\alpha}$ regularity result for the pressure for weak solutions of the two-dimensional "incompressible Euler equations" when the fluid velocity enjoys the same type of…
The global well-posedness and inviscid limit are investigated for the fluid-particle interaction system, described by the Navier-Stokes equations for the inhomogeneous incompressible viscous flows coupled with the Vlasov-Fokker-Planck…