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In this paper, we consider a two-dimensional fluid-rigid body problem. The motion of the fluid is modelled by the Navier-Stokes equations, whereas the dynamics of the rigid body is governed by the conservation laws of linear and angular momentum. The rigid body is supposed to be an infinite cylinder of circular cross-section. Our main result is the existence and uniqueness of global strong solutions. Mathematics Subject Classification (2000). 35Q30, 76D03, 76D05.

Hemolysis of human erythrocytes induced by free radicals initiated from water-soluble, 2,2'-azobis(amidinopropane) dihydrochloride (AAPH) has been investigated. The formation of the radical detected as DMPO (5,5-dimethyl-1-pyrroline N-oxide) adduct depended on temperature and AAPH concentration in a similar manner as hemolysis. The curve for the formation of DMPO--radical adduct, however, did not correspond directly to the hemolysis curve. The product of thiobarbituric acid-reactive materials, which reflect the extent of lipid peroxidation, could not be related directly to the hemolysis curve, too. During the hemolysis, the fluidity of the erythrocyte membrane did not change in appearance. To study whether band 3 proteins participate in the hemolysis or not, eosin-5-maleimide (EMI)-labeled ghosts were incubated in the presence of AAPH. High molecular weight band 3 was formed, and the induced circular dichrosim spectrum of the bound EMI was changed, indicating a conformational change of band 3. It was observed that ascorbic acid suppressed the hemolysis and the oxidation of band 3 dose dependently to produce an induction period. This result shows that specifically blocking band 3 oxidation inhibits the hemolysis, despite lipid peroxidation. Further, it was observed that the EMI-labeled erythrocytes revealed distinct clusters by incubation with AAPH. This means a redistribution of band 3 proteins to form hemolytic holes in the membrane. However, the time course of the conformational change of band 3 during the redistribution was not also correspondent to the hemolysis curve. These results indicate that either lipid peroxidation or redistribution of oxidized band 3 is not attributed only by itself to the hemolysis. Thus, the hemolysis was interpreted by a simple competitive reaction model between lipid peroxidation and redistribution of oxidized band 3. This model explained well the hemolysis curves.

Let A : D(A) → X be the generator of an analytic semigroup and B : V → [D(A *)] ′ a relatively bounded control operator. In this paper, we consider the stabilization of the system y ′ = Ay +Bu where u is the linear combination of a family (v1,. .. , vK). Our main result shows that if (A * , B *) satisfies a unique continuation property and if K is greater or equal to the maximum of the geometric multiplicities of the unstable modes of A, then the system is generically stabilizable with respect to the family (v1,. .. , vK). With the same functional framework, we also prove the stabilizability of a class of nonlinear systems when using feedback or dynamical controllers. We apply these results to stabilize the Navier-Stokes equations in 2D and in 3D by using boundary controls.

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