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We consider the Navier–Stokes equations in an aperture domain of the three‐dimensional Euclidean space. We are interested in proving the existence of regular solutions corresponding to small initial data and flux through the aperture. The flux is assumed to be smooth and bounded on (0, +∞). As a consequence, we prove the existence of a time‐periodic solution corresponding to a time‐periodic flux through the aperture. Finally, we compare our solution with a solution belonging to a wider class, showing that, if such a solution does exist, then the two solutions coincide. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
3.
We show that, in general, the solutions to the initial-boundary value problem for the Navier-Stokes equations under a widely adopted Navier-type slip
boundary condition do not converge, as the viscosity goes to zero, to the solution of the Euler equations under the classical
zero-flux boundary condition, and same smooth initial data, in any arbitrarily small neighborhood of the initial time. Convergence
does not hold with respect to any space-topology which is sufficiently strong as to imply that the solution to the Euler equations
inherits the complete slip type boundary condition. In our counter-example Ω is a sphere, and the initial data may be infinitely
differentiable. The crucial point here is that the boundary is not flat. In fact (see Beir?o da Veiga et al. in J Math Anal
Appl 377:216–227, 2011) if
W = \mathbb R3+,{\,\Omega = \mathbb R^3_+,} convergence holds in
C([0,T]; Wk,p(\mathbb R3+)){C([0,T]; W^{k,p}(\mathbb R^3_+))}, for arbitrarily large k and p. For this reason, the negative answer given here was not expected. 相似文献
4.
MMP-9, human matrix metalloproteinase 9, belongs to the family of zinc-dependent peptide-bond hydrolases and is involved in the degradation of the extracellular matrix (ECM). In clinics, it is well known that elevated MMP-9 serum levels are associated with cardiovascular dysfunctions, several aspects of the physiology and pathology of the central nervous system, neuropsychiatric disorders and degenerative diseases related to brain tumors, and excitotoxic/neuroinflammatory processes. Due to the large interest of diagnostics in this protein, efforts to set up sensitive methods to detect MMP-9 for early diagnosis of a number of metabolic alterations are rapidly increasing. In this panorama, biosensors could play a key role; therefore we explored for the first time the development of an aptamer-based piezoelectric biosensor for a sensitive, label free, and real time detection of MMP-9. The detecting strategy involved two different aptamers in a sandwich-like approach able to detect down to 100 pg mL−1 (1.2 pM) of MMP-9 as detection limit in standard solution. As proof of principle, commercial serum was investigated in terms of possible interferents, their identification and role in MMP-9 detection. The estimated detection limit for MMP-9 is about 560 pg mL−1 (6.8 pM) in untreated serum. 相似文献
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The paper is concerned with the IBVP of the Navier–Stokes equations. The goal is to evaluate the possible gap between the energy equality and the energy inequality deduced for a weak solution. This kind of analysis is new and the result is a natural continuation and improvement of a result obtained by the same authors in Crispo et al. (Some new properties of a suitable weak solution to the Navier–Stokes equations. arXiv:1904.07641).
相似文献6.
Francesca Crispo 《Journal of Mathematical Analysis and Applications》2008,341(1):559-574
We consider the motion of an incompressible non-Newtonian fluid with shear dependent viscosity. We extend and improve the results obtained in the recent paper by Crispo [F. Crispo, Shear thinning viscous fluids in cylindrical domains. Regularity up to the boundary, J. Math. Fluid Mech., in press], concerning the case of the motion between two coaxial cylinders, to the case of a full cylinder. Actually we prove boundary regularity for solutions to the stationary Dirichlet problem with zero boundary data. 相似文献
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Dewar PJ MacGillivray TF Crispo SM Smith-Palmer T 《Journal of colloid and interface science》2000,228(2):253-258
Silica spheres were prepared by the St?ber method, and the method of labeling with pyrene, using aminopropylysilane as the linking agent, was optimized. Excimers between particles were formed when high concentrations of label were used. Both surfactant and polyelectrolyte addition were able to cause floc formation when added to suspensions of the silica, but only the surfactant changed the I(1)/I(3) ratio and diminished excimer formation. Copyright 2000 Academic Press. 相似文献
8.
Francesca Crispo 《Journal of Mathematical Fluid Mechanics》2008,10(3):311-325
We consider the motion of a non-Newtonian fluid with shear dependent viscosity between two cylinders. We prove regularity
results for the second derivatives of the velocity and the first derivatives of the pressure up to the boundary. A similar
problem is studied in reference [2] in the case of a flat boundary. Here we extend the techniques applied in [2] to cylindrical
coordinates.
相似文献
9.
Francesca Crispo 《Acta Appl Math》2014,130(1):237-250
In this paper we study the nonlinear Klein-Gordon-Maxwell system $$\left \{\begin{array}{l@{\quad}l} -\Delta u+V(x)u-(2\omega+\phi)\phi u=f(x,u),&x\in{\mathbb{R}}^3,\\ \Delta \phi=(\omega+\phi)u^2,&x\in{\mathbb{R}}^3. \end{array} \right . $$ By means of a variant fountain theorem and the symmetric mountain pass theorem, we obtain the existence of infinitely many large energy solutions. 相似文献
10.
Francesca Crispo Alfonsina Tartaglione 《Mathematical Methods in the Applied Sciences》2007,30(12):1375-1401
We consider the problem of the asymptotic behaviour in the L2‐norm of solutions of the Navier–Stokes equations. We consider perturbations to the rest state and to stationary motions. In both cases we study the initial‐boundary value problem in unbounded domains with non‐compact boundary. In particular, we deal with domains with varying and possibly divergent exits to infinity and aperture domains. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献