# Existence and nonexistence results for critical growth biharmonic elliptic equations

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We consider the stability of stationary solutions w for the exterior Navier-Stokes flows with a nonzero constant velocity uâˆž at infinity. For uâˆž = 0 with nonzero stationary solution w, Chen (1993), Kozono and Ogawa (1994), and Borchers and Miyakawa (1995) have studied the temporal...

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The axially symmetric solutions to the Navier-Stokes equations are studied. Assume that either the radial component ( v) of the velocity belongs to L(0, T; L(O)) or v/ r belongs to L(0, T; L(O)), where O is a neighborhood of the axis of symmetry. Assume additionally that there exist subdomains...

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We investigate the incompressible Navier-Stokes equations with variable density. The aim is to prove existence and uniqueness results in the case of discontinuous initial density. In dimension n = 2,3, assuming only that the initial density is bounded and bounded away from zero, and that the...

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In this paper we establish the uniform local-in-time existence and uniqueness of classical solutions to the density-dependent Navier-Stokes-Maxwell system. We then apply this uniform result to investigate the zero dielectric constant limit and the vanishing viscosity limit to...

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We consider the Navierï¿½Stokes equations in the thin 3D domain $${\mathbb{T}}_2 \times (0, \epsilon)$$ , where $${\mathbb{T}}_2$$ is a two-dimensional torus. The equation is perturbed by a non-degenerate random kick force. We establish that, firstly, when e ï¿½ 1, the equation has a...

- An analysis model of pulsatile blood flow in arteries. Liu Zhao-rong; Xu Gang; Chen Yong; Teng Zhong-zhao; Qin Kai-rong // Applied Mathematics & Mechanics;Feb2003, Vol. 24 Issue 2, p230
Blood flow in artery was treated as the flow under equilibrium state (the steady flow under mean pressure) combined with the periodically small pulsatile flow. Using vascular strain energy function advanced by Fung, the vascular stress-strain relationship under equilibrium state was analyzed and...