33,205 research outputs found
Existence of weak solutions for the generalized Navier-Stokes equations with damping
In this work we consider the generalized Navier-Stokes equations with the presence of a damping term in the momentum equation. The problem studied here derives from the set of equations which govern isothermal flows of incompressible and homogeneous non-Newtonian fluids. For the generalized Navier-Stokes problem with damping, we prove the existence of weak solutions by using regularization techniques, the theory of monotone operators and compactness arguments together with the local decomposition of the pressure and the Lipschitz-truncation method. The existence result proved here holds for any and any sigma > 1, where q is the exponent of the diffusion term and sigma is the exponent which characterizes the damping term.MCTES, Portugal [SFRH/BSAB/1058/2010]; FCT, Portugal [PTDC/MAT/110613/2010]info:eu-repo/semantics/publishedVersio
On shape optimization for compressible isothermal Navier-Stokes equations
The steady state system of isothermal Navier-Stokes equations is considered in two dimensional domain including an obstacle. The shape optimisation problem of drag minimisation with respect to the admissible shape of the obstacle is defined. The generalized solutions for the Navier-Stokes equations are introduced. The existence of an optimal shape is proved in the class of admissible domains. In general the solution to the problem under consideration is not unique
On the Inviscid Limit of the 3D Navier-Stokes Equations with Generalized Navier-slip Boundary Conditions
In this paper, we investigate the vanishing viscosity limit problem for the
3-dimensional (3D) incompressible Navier-Stokes equations in a general bounded
smooth domain of with the generalized Navier-slip boundary conditions
(\ref{VSg}). Some uniform estimates on rates of convergence in
and of the solutions to the
corresponding solutions of the idea Euler equations with the standard slip
boundary condition are obtained
Generalized Navier-Stokes equations with nonlinear anisotropic viscosity
The purpose of this work is to study the generalized Navier-Stokes equations with nonlinear viscosity that, in addition, can be fully anisotropic. Existence of very weak solutions is proved for the associated initial and boundary-value problem, supplemented with no-slip boundary conditions. We show that our existence result is optimal in some directions provided there is some compensation in the remaining directions. A particular simplification of the problem studied here, reduces to the Navier-Stokes equations with (linear) anisotropic viscosity used to model either the turbulence or the Ekman layer in atmospheric and oceanic fluid flows.Portuguese Foundation for Science and Technology, PortugalPortuguese Foundation for Science and Technology [UID/MAT/04561/2019][SFRH/BSAB/135242/2017
Analyticity for the (generalized) Navier-Stokes equations with rough initial data
We study the Cauchy problem for the (generalized) incompressible
Navier-Stokes equations \begin{align} u_t+(-\Delta)^{\alpha}u+u\cdot \nabla u
+\nabla p=0, \ \ {\rm div} u=0, \ \ u(0,x)= u_0. \nonumber \end{align} We show
the analyticity of the local solutions of the Navier-Stokes equation
() with any initial data in critical Besov spaces
with
and the solution is global if is sufficiently small in
. In the case , the analyticity
for the local solutions of the Navier-Stokes equation () with any
initial data in modulation space is obtained.
We prove the global well-posedness for a fractional Navier-stokes equation
() with small data in critical Besov spaces
and show the
analyticity of solutions with small initial data either in
or in
.
Similar results also hold for all .Comment: 31 page
On shape optimization for compressible isothermal Navier-Stokes equations
The steady state system of isothermal Navier-Stokes equations is considered in two dimensional domain including an obstacle. The shape optimisation problem of drag minimisation with respect to the admissible shape of the obstacle is defined. The generalized solutions for the Navier-Stokes equations are introduced. The existence of an optimal shape is proved in the class of admissible domains. In general the solution to the problem under consideration is not unique
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