arXiv subjects

Cilon Perusato

Publications and source records attributed to Cilon Perusato.

5 recordsLinked to original sources

arXiv2025

Exponential blow-up of mild solutions to the fractional Boussinesq equations in the Gevrey class

This work establishes conditions for the existence and uniqueness of local mild solutions to the Boussinesq equations with fractional dissipations in Sobolev-Gevrey spaces. We prove that a unique mild solution exists in an appropriate Sobolev-Gevrey class and analyze its behavior up to the maximal time of existence. In particular, we derive quantitative lower bounds describing how the norm of the solution must blow up as it approaches a finite maximal time. As a corollary, we deduce that the solution exhibits exponential growth.

math.AP↗

arXiv2022

Strong Alignment of Micro-rotation and Vorticity in 3D Micropolar Flows

Rigid particles suspended on a micropolar fluid provide microstructure that coexists and interacts with the local rotation of the fluid given by the vorticity. In this work we prove that the particles' angular velocity and the vorticity strongly align for large times. We provide average and supnorm estimates for the decay rate of the difference between these two vectors, which measures the alignment.

math.AP↗

arXiv2020

Sharp decay estimates and asymptotic behaviour for 3D magneto-micropolar fluids

We characterize the $L^2$ decay rate of solutions to the 3D magneto-micropolar system in terms of the decay character of the initial datum. Due to a linear damping term, the micro-rotational field has a faster decay rate. We also address the asymptotic behaviour of solutions by comparing them to solutions to the linear part. As a result of the linear damping, the difference between the micro-rotational field and its linear part also decays faster. As part of the proofs of these results, we prove estimates for the derivatives of solutions which might be of independent interest.

math.AP↗

arXiv2017

Asymptotic behavior of global weak solutions for the micropolar dynamics in $L^{2}(\mathbb{R}^{3})$

In this paper the long time behavior of the micropolar fluid equations energy on three dimensional space are studied. We show that $ \| (u,w)(\cdot,t) \|_{{L^{2}(\mathbb{R}^{3})}} \to 0 $ as $t \to \infty$ for Leray-Hopf's global weak solutions in inviscid vortex case. Moreover, when the vortex viscosity are considered, i.e., $\chi >0$, we obtain a (faster) decay for micro-rotational field: $ \| w (\cdot,t) \|_{{L^{2}(\mathbb{R}^{3})}} = o(t^{-1/2})$.

math.AP↗

arXiv2017

Decay Rates of global weak solutions for the MHD equations in $\dot{\mbox{\boldmath{$H$}}}^{s}(\mathbb{R}^n)$

We show that $t^{s/2} \Vert (\mbox{\boldmath $u$},\mbox{\boldmath $b$})(.,t)\Vert_{\dot{H}(\mathbb{R}^{n})} \rightarrow 0,$ as $t\rightarrow \infty$ for Leray solutions $(\mbox{\boldmath $u$}, \mbox{\boldmath $b$})(.,t)$ of the incompressible MHD equations, where $2 \leq n \leq 4$ and $s \geq 0.$ As a corollary of main result described previously we have also that $\lim_{t\rightarrow\infty} t^{\frac{n}{2} - \frac{n}{2q}} \Vert(\mbox{\boldmath $u$},\mbox{\boldmath $b$})(.,t)\Vert_{L^{q}(\mathbb{R}^{n})} = 0, 2\leq q\leq \infty.$

math.AP↗