arXiv subjects

Jiaojiao Pan

Publications and source records attributed to Jiaojiao Pan.

7 recordsLinked to original sources

arXiv2026

Homogenization of the Navier-Stokes-Cahn-Hilliard system in the small-hole regime

This paper investigates the homogenization of the 3D Navier--Stokes--Cahn--Hilliard (NSCH) system in domains containing a large number of solid obstacles (named holes). Each hole has diameter of order $\varepsilon^α(α>3)$, where $\varepsilon > 0$ denotes the small length scale for inter-hole separation. Both viscosity and mobility depend on the phase-field variable. We establish two distinct asymptotic regimes: if the capillary strength $λ_\varepsilon\to λ>0$ as $\varepsilon\to 0$, the limit system coincides with the original NSCH system; if $λ_\varepsilon\to 0$ as $\varepsilon\to 0$, the scaled velocity, phase field and chemical potential converge to a weak solution to a Stokes--Cahn--Hilliard (SCH) system. To the best of our knowledge, this work constitutes the first rigorous homogenization analysis for evolutionary NSCH flows with phase-dependent viscosity and mobility under the subcritical hole scaling.

math.AP↗

arXiv2026

Homogenization of a non-homogeneous incompressible heat-conducting fluid in perforated domains

This paper provides the study of the homogenization of the 3D non-homogeneous incompressible heat-conducting fluid in perforated domains with holes of subcritical size, where the viscosity and the heat conductivity coefficient are assumed to depend on the temperature. The diameter of the holes is of order $\varepsilon^α \ (α>3)$, where $\varepsilon > 0$ is a small parameter that measures the mutual distance between the holes. We prove that as $\varepsilon\to 0$, the limit behavior of velocity, density and temperature is governed by the original system in homogeneous domain without holes.

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arXiv2025

Qualitative derivation of a density dependent incompressible Darcy law

This paper provides the first study of the homogenization of the 3D non-homogeneous incompressible Navier--Stokes system in perforated domains with holes of supercritical size. The diameter of the holes is of order $\varepsilon^α \ (1<α<3)$, where $\varepsilon > 0$ is a small parameter measuring the mutual distance between the holes. We show that as $\varepsilon\to 0$, the asymptotic limit behavior of velocity and density is governed by Darcy's law under the assumption of a strong solution of the limiting system. Moreover, convergence rates are obtained. Finally, we show the existence of strong solutions to the inhomogeneous incompressible Darcy law, which might be of independent interest.

math.AP↗

arXiv2025

Homogenization of Inhomogeneous Incompressible Navier-Stokes Equations in Domains with Very Tiny Holes

In this paper, we study the homogenization problems of $3D$ inhomogeneous incompressible Navier-Stokes system perforated with very tiny holes whose diameters are much smaller than their mutual distances. The key is to establish the equations in the homogeneous domain without holes for the zero extensions of the weak solutions. This allows us to derive time derivative estimates and show the strong convergence of the density and the momentum by Aubin-Lions type argument. For the case of small holes, we finally show the limit equations remain unchanged in the homogenization limit.

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arXiv2024

Homogenization of Non-homogeneous Incompressible Navier-Stokes System in Critically Perforated Domains

In this paper, we study the homogenization of 3D non-homogeneous incompressible Navier-Stokes system in perforated domains with holes of critical size. The diameter of the holes is of size ε^3, where εis a small parameter measuring the mutual distance between the holes. We show that when εtends to 0, the velocity and density converge to a solution of the non-homogeneous incompressible Navier-Stokes system with a friction term of Brinkman type.

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arXiv2022

A note on separation conditions of resonance sets in the instability analysis for high-frequency oscillations in geometric optics

In this paper, we study the instability of highly-oscillating solutions to semi-linear hyperbolic systems. A instability criterion was given in \cite{Lu} under rather strong separation conditions of resonance sets: coupled resonance sets are pairwise disjoint. Here we show that such separation conditions in \cite{Lu} can be relaxed: one of the coupled non-transparent resonance sets is allowed to intersect with at most two others. We obtain the same instability criterion as in \cite{Lu}. Finally, we give some applications to coupled Klein-Gordon systems with equal masses and nonlinear terms specified particularly, where on the intersections of resonance sets, the related interaction coefficients are non-transparent.

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arXiv2021

Homogenization problems for the compressible Navier-Stokes system in 2D perforated domains

In this paper, we study the homogenization problems for the stationary compressible Navier-Stokes system in a bounded 2D domain, where the domain is perforated with very tiny holes (or obstacles) whose diameters are much smaller than their mutual distances. We obtain that the process of homogenization doesn't change the motion of the fluids. From another point of view, we obtain the same system of equations in the asymptotic limit. It is the first result of homogenization problem in the compressible case in 2 dimensions.

math.AP↗