Navier-Stokes equation solutions

We study the stability of a flexible beam that is clamped at one end and free at the other; a mass is also attached to the free end of the beam. To stabilize this system we apply a boundary control force at the free end of the beam. We prove that the closed-loop system is well-posed and is exponentially stable. We the…

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• NECAT POLAT

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• SERKAN ÖZGEN

We consider a flexible spacecraft modelled as a rigid body rotating in inertial space; a light flexible beam is clamped to the rigid body at one end and is free at the other. The equations of motion are obtained by using free-body diagrams. It is shown that suitable boundary controls applied to the free end of the bea…

We consider a system described by the Euler-Bernoulli beam equation. For stabilization, we propose a dynamic boundary controller applied at the free end of the system. The transfer function of the controller is a marginally stable positive real function which may contain poles on the imaginary axis. We then give vario…

We consider the 2D Navier–Stokes–Voight equation in an unbounded strip-like domain. It is shown that the semigroup generated by this equation has a global attractor in weighted Sobolev spaces.

• MUSTAFA POLAT

We investigate the numerical approximation of (discontinuous) entropy solutions to nonlinear hyperbolic conservation laws posed on a Lorentzian manifold.Our main result establishes the convergence of monotone and first-order finite volume schemes for a large class of (space and time) triangulations.The proof relies on…

• BAVER OKUTMUŞTUR

We present some consequences of non-anomalous propagation requirements on various massless fields. Among the models of nonlinear electrodynamics we show that only the Maxwell and Born-Infeld models also obey duality invariance. Separately we show that, for actions depending only on the invariant, the permitted models…

• BAHTİYAR ÖZGÜR SARIOĞLU

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• EMRULLAH YAŞAR

The main aim of this paper is to study the dynamic transitions in flows described by the two-dimensional, barotropic vorticity equation in a periodic zonal channel. In [Z.-M. Chen et al., SIAM J. Appl. Math., 64 (2003), pp. 343--368], the existence of a Hopf bifurcation in this model as the Reynolds number crosses a c…

• MUSTAFA TAYLAN ŞENGÜL

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For the Lamé system, we prove in the three-dimensional case that both Lamé coefficients are uniquely recovered from partial Cauchy data on an arbitrary open subset of the boundary provided that the coefficient μ is a constant.

• MASAHİRO YAMAMOTO