The existence of weak solutions for steady flows of electrorheological fluids with nonhomogeneous Dirichlet boundary condition

2017 ◽  
Vol 163 ◽  
pp. 146-162 ◽  
Author(s):  
Cholmin Sin
Keyword(s):  
Boundary Condition ◽  
Weak Solutions ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Electrorheological Fluids ◽  
Steady Flows ◽  
Existence Of Weak Solutions

Sequences of Weak Solutions for Non-Local Elliptic Problems with Dirichlet Boundary Condition

2014 ◽  
Vol 57 (3) ◽  
pp. 779-809 ◽  
Author(s):  
Giovanni Molica Bisci ◽  
Pasquale F. Pizzimenti
Keyword(s):  
Boundary Condition ◽  
Dirichlet Problem ◽  
Variational Methods ◽  
Weak Solutions ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Infinitely Many Solutions ◽  
Distinct Sequence ◽  
Non Local ◽  
Kirchhoff Type Problems

AbstractIn this paper the existence of infinitely many solutions for a class of Kirchhoff-type problems involving the p-Laplacian, with p > 1, is established. By using variational methods, we determine unbounded real intervals of parameters such that the problems treated admit either an unbounded sequence of weak solutions, provided that the nonlinearity has a suitable behaviour at ∞, or a pairwise distinct sequence of weak solutions that strongly converges to 0 if a similar behaviour occurs at 0. Some comparisons with several results in the literature are pointed out. The last part of the work is devoted to the autonomous elliptic Dirichlet problem.

scholarly journals Global weak solutions for a kinetic-fluid model with local alignment force in a bounded domain

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Fucai Li ◽  
Yue Li
Keyword(s):  
Boundary Condition ◽  
Bounded Domain ◽  
Weak Solutions ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Stokes Equations ◽  
Fluid Model ◽  
Navier Stokes ◽  
Local Alignment ◽  
Fokker Planck

<p style='text-indent:20px;'>We study a kinetic-fluid model in a <inline-formula><tex-math id="M1">\begin{document}$ 3D $\end{document}</tex-math></inline-formula> bounded domain. More precisely, this model is a coupling of the Vlasov-Fokker-Planck equation with the local alignment force and the compressible Navier-Stokes equations with nonhomogeneous Dirichlet boundary condition. We prove the global existence of weak solutions to it for the isentropic fluid (adiabatic coefficient <inline-formula><tex-math id="M2">\begin{document}$ \gamma&gt; 3/2 $\end{document}</tex-math></inline-formula>) and hence extend the existence result of Choi and Jung [Asymptotic analysis for a Vlasov-Fokker-Planck/Navier-Stokes system in a bounded domain, arXiv: 1912.13134v2], where the velocity of the fluid is supplemented with homogeneous Dirichlet boundary condition.</p>

On steady flows of fluids with pressure– and shear–dependent viscosities

2005 ◽  
Vol 461 (2055) ◽  
pp. 651-670 ◽  
Author(s):  
M. Franta ◽  
J. Málek ◽  
K. R. Rajagopal
Keyword(s):  
Shear Rate ◽  
Weak Solutions ◽  
Velocity Gradient ◽  
Dirichlet Boundary ◽  
Incompressible Fluids ◽  
Dirichlet Boundary Conditions ◽  
Steady Flows ◽  
Existence Of Weak Solutions ◽  
Wide Range ◽  
Homogeneous Dirichlet Boundary Conditions

There are many technologically important problems such as elastohydrodynamics which involve the flows of a fluid over a wide range of pressures. While the density of the fluid remains essentially constant during these flows whereby the fluid can be approximated as being incompressible, the viscosity varies significantly by several orders of magnitude. It is also possible that the viscosity of such fluids depends on the shear rate. Here we consider the flows of a class of incompressible fluids with viscosity that depends on the pressure and shear rate. We establish the existence of weak solutions for the steady flows of such fluids subjected to homogeneous Dirichlet boundary conditions and to specific body forces that are not necessarily assumed to be small. A novel aspect of the study is the manner in which we treat the pressure that allows us to establish its compactness, as well as that of the velocity gradient. The method draws upon the physics of the problem, namely that the notion of incompressibility is an idealization that is attained by letting the compressibility of the fluid to tend to zero.

scholarly journals A New Proof of Existence of Positive Weak Solutions for Sublinear Kirchhoff Elliptic Systems with Multiple Parameters

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Salah Mahmoud Boulaaras ◽  
Rafik Guefaifia ◽  
Bahri Cherif ◽  
Sultan Alodhaibi
Keyword(s):  
Boundary Condition ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Weak Solutions ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Elliptic Systems ◽  
Multiple Parameters

This paper deals with the study of the existence of weak positive solutions for sublinear Kirchhoff elliptic systems with zero Dirichlet boundary condition in bounded domain Ω⊂ℝN by using the subsuper solutions method.

scholarly journals On some classes of generalized Schrödinger equations

2020 ◽  
Vol 10 (1) ◽  
pp. 522-533
Author(s):  
Amanda S. S. Correa Leão ◽  
Joelma Morbach ◽  
Andrelino V. Santos ◽  
João R. Santos Júnior
Keyword(s):  
Boundary Condition ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Laplacian Operator ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nontrivial Solutions ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Stationary Problems

Abstract Some classes of generalized Schrödinger stationary problems are studied. Under appropriated conditions is proved the existence of at least 1 + $\begin{array}{} \sum_{i=2}^{m} \end{array}$ dim Vλi pairs of nontrivial solutions if a parameter involved in the equation is large enough, where Vλi denotes the eigenspace associated to the i-th eigenvalue λi of laplacian operator with homogeneous Dirichlet boundary condition.

Sign in / Sign up

Export Citation Format

Share Document