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We address a system of equations modeling an incompressible fluid interacting with an elastic body. We prove the local existence when the initial velocity belongs to the space$$H^{1.5+\epsilon }$$$H^{1.5+ϵ}$and the initial structure velocity is in$$H^{1+\epsilon }$$$H^{1+ϵ}$, where$$\epsilon \in (0, 1/20)$$$ϵ\in (0,1/20)$.

We derivea prioriestimates for the compressible free boundary Euler equations in the case of a liquid without surface tension. We provide a new weighted functional framework which leads to the improved regularity of the flow map by using the Hardy inequality. One of main ideas is to decompose the initial density function. It is worth mentioning that in our analysis we do not need the higher order wave equation for the density.

We address a system of equations modeling a compressible fluid interacting with an elastic body in dimension three. We prove the local existence and uniqueness of a strong solution when the initial velocity belongs to the space$$H^{2+\epsilon }$$$H^{2+ϵ}$and the initial structure velocity is in$$H^{1.5+\epsilon }$$$H^{1.5+ϵ}$, where$$\epsilon \in (0,1/2)$$$ϵ\in (0,1/2)$.

We address the Mach limit problem for the Euler equations in an exterior domain with an analytic boundary. We first prove the existence of tangential analytic vector fields for the exterior domain with constant analyticity radii and introduce an analytic norm in which we distinguish derivatives taken from different directions. Then we prove the uniform boundedness of the solutions in the analytic space on a time interval independent of the Mach number, and Mach limit holds in the analytic norm. The results extend more generally to Gevrey initial data with convergence in a Gevrey norm.

This article presents the fabrication of super‐hydrophobic cotton fabric using titanium dioxide nanoparticles and tetraethyl orthosilicate, alongside control samples modified by 1H,1H,2H,2H‐perfluorooctyltriethoxysilane. The samples were analyzed using scanning electron microscopy and Fourier transform infrared spectrometry, and then, the water contact angles were measured. Moreover, the durability of the hydrophobic surface was examined by measuring the abrasion resistance and laundering durability. For the tetraethyl orthosilicate‐treated fabric, the water contact angle reached 150.3°, whereas that for the 1H,1H,2H,2H‐perfluorooctyltriethoxysilane‐treated fabric was 154.1°. After 300 abrasion cycles (or 40 min of laundering), the water contact angles of cotton fabrics treated with a 20% tetraethyl orthosilicate treatment solution dropped by 6.67% (or 2.86%). Therefore, hydrophobic cotton fabrics can be obtainedviatreatment with tetraethyl orthosilicate solution, which is more environmentally friendly than that obtainedviafluorosilanes such as 1H,1H,2H,2H‐perfluorooctyltriethoxysilane. J. VINYL ADDIT. TECHNOL., 26:3–9, 2020. © 2019 Society of Plastics Engineers