On a p x -Biharmonic Kirchhoff Problem with Navier Boundary Conditions

In this article, we study the existence of solutions for nonlocal p x -biharmonic Kirchhoff-type problem with Navier boundary conditions. By different variational methods, we determine intervals of parameters for which this problem admits at least one nontrivial solution.

Remarks on the 3D Stokes eigenvalue problem under Navier boundary conditions

We study the Stokes eigenvalue problem under Navier boundary conditions in $$C^{1,1}$$ C 1 , 1 -domains $$\Omega \subset \mathbb {R}^3$$ Ω ⊂ R 3 . Differently from the Dirichlet boundary conditions, zero may be the least eigenvalue. We fully characterize the domains where this happens and we show that the ball is the unique domain where the zero eigenvalue is not simple, it has multiplicity three. We apply these results to show the validity/failure of a suitable Poincaré-type inequality. The proofs are obtained by combining analytic and geometric arguments.

Multiple Solutions for a Nonlocal Elliptic Problem Involving p x , q x -Biharmonic Operator

In this paper, using the variational principle, the existence and multiplicity of solutions for p x , q x -Kirchhoff type problem with Navier boundary conditions are proved. At the same time, the sufficient conditions for the multiplicity of solutions are obtained.

A Hopf Bifurcation in the Planar Navier–Stokes Equations

We consider the Navier–Stokes equation for an incompressible viscous fluid on a square, satisfying Navier boundary conditions and being subjected to a time-independent force. As the kinematic viscosity is varied, a branch of stationary solutions is shown to undergo a Hopf bifurcation, where a periodic cycle branches from the stationary solution. Our proof is constructive and uses computer-assisted estimates.

Regularity for the 3D evolution Navier-Stokes equations under Navier boundary conditions in some Lipschitz domains

<p style='text-indent:20px;'>For the evolution Navier-Stokes equations in bounded 3D domains, it is well-known that the uniqueness of a solution is related to the existence of a regular solution. They may be obtained under suitable assumptions on the data and smoothness assumptions on the domain (at least <inline-formula><tex-math id="M1">\begin{document}$ C^{2,1} $\end{document}</tex-math></inline-formula>). With a symmetrization technique, we prove these results in the case of Navier boundary conditions in a wide class of merely <i>Lipschitz domains</i> of physical interest, that we call <i>sectors</i>.</p>