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Yongzhong Sun

Publications and source records attributed to Yongzhong Sun.

17 recordsLinked to original sources
arXiv2026

Remarks on Linear Growth of Vorticity Gradients and Support Diameters for 2D Euler Flow in Half-Plane

It has been conjectured that generic smooth solutions of the two-dimensional Euler equation exhibit linear growth of vorticity gradients. We prove an elementary arbitrary-background perturbation principle in the odd symmetric setting. More precisely, for any compactly supported nonnegative function in the half-plane, one can find an arbitrarily small smooth nonnegative perturbation whose associated solution undergoes linear-in-time filamentation in the quadrant. The main ingredients are the lower bound of the center of mass given by Iftimie-Sideris-Gamblin, and the velocity estimate for the sparse part to capture those slowly moving particles.

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arXiv2025

Weak solutions to a compressible viscous non-resistive MHD equations with general boundary data

This paper is concerned with a compressible MHD equations describing the evolution of viscous non-resistive fluids in piecewise regular bounded Lipschitz domains. Under the general inflow-outflow boundary conditions, we prove existence of global-in-time weak solutions with finite energy initial data. The present result extends considerably the previous work by Li and Sun [\emph{J. Differential Equations.}, 267 (2019), pp. 3827-3851], where the homogeneous Dirichlet boundary condition for velocity field is treated. The proof leans on the specific mathematical structure of equations and the recently developed theory of open fluid systems. Furthermore, we establish the weak-strong uniqueness principle, namely a weak solution coincides with the strong solution on the lifespan of the latter provided they emanate from the same initial and boundary data. This basic property is expected to be useful in the study of convergence of numerical solutions.

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arXiv2024

Unconditional stability of equilibria in thermally driven compressible fluids

We show that small perturbations of the spatially homogeneous equilibrium of a thermally driven compressible viscous fluid are globally stable. Specifically, any weak solution of the evolutionary Navier--Stokes--Fourier system driven by thermal convection converges to an equilibrium as time goes to infinity. The main difficulty to overcome is the fact the problem does not admit any obvious Lyapunov function. The result applies, in particular, to the Rayleigh--B\' enard convection problem.

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arXiv2023

On asymptotic stability of the 3D Boussinesq equations without thermal conduction

We investigate the asymptotic stability of solution to Boussinesq equations without thermal conduction with the initial data near a specific stationary solution in the three--dimensional domain $Ω= \mathbb{R}^{2}\times (0,1)$. It is shown that the solution starting from a small perturbation to the stationary solution converges to it with explicit algebraic rates as time tends to infinity.

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arXiv2021

Asymptotic stability of the 2D Boussinesq equations without thermal conduction

This paper is concerned with the asymptotic stability of certain stationary solution to Boussinesq equations without thermal conduction in the infinite flat strip $Ω=\mathbb{R}\times (0,1)$. It is shown that the solution starting from initial data close to the stationary solution will converge to it with explicit algebraic rates as time tends to infinity.

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arXiv2020

On global-in-time weak solutions to a 2D full compressible non-resistive MHD system

In this paper, we consider a two-dimensional non-resistive magnetohydrodynamic model, taking the fluctuation of absolute temperature into account. Combining the method of weak convergence developed by Lions [20], Feireisl et al. [7, 8] from compressible Navier-Stokes(- Fourier) system and the new technique of variable reduction proposed by Vasseur et al. [26] and refined by Novotny et al. [22] from compressible two-fluid models, weak solutions are shown to exist globally in time with finite energy initial data. The result is the first one on global solvability to full compressible, viscous, non-resistive magnetohydrodynamic system in multi-dimensions with large initial data.

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arXiv2019

Low Mach number limit on thin domains

We consider the compressible Navier-Stokes system describing the motion of a viscous fluid confined to a straight layer $Ω_δ=(0,δ)\times\mathbb{R}^2$. We show that the weak solutions in the 3D domain converge strongly to the solution of the 2D incompressible Navier-Stokes equations (Euler equations) when the Mach number $ε$ tends to zero as well as $δ\rightarrow 0$ (and the viscosity goes to zero).

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arXiv2019

Global weak solutions to a two-dimensional compressible MHD equations of viscous non-resistive fluids

We consider a two-dimensional MHD model describing the evolution of viscous, compressible and electrically conducting fluids under the action of vertical magnetic field without resistivity. Existence of global weak solutions is established for any adiabatic exponent γ>1. Inspired by the approximate scheme proposed in [15], we consider a two-level approximate system with artificial diffusion and pressure term. At the first level, we prove global well-posedness of the regularized system and establish uniform-in-εestimates to the regular solutions. At the second level, we show global existence of weak solutions to the system with artificial pressure by sending εto 0 and deriving uniform-in-δestimates. Then global weak solution to the original system is constructed by vanishing δ. The key issue in the limit passage is the strong convergence of approximate sequence of the density and magnetic field. This is accomplished by following the technique developed in [15, 26] and using the new technique of variable reduction developed by Vasseur et al. [33] in order to handle the cross terms.

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arXiv2018

Large time behavior for a compressible two-fluid model with algebraic pressure closure and large initial data

In this paper, we consider a compressible two-fluid system with a common velocity field and algebraic pressure closure in dimension one. Existence, uniqueness and stability of global weak solutions to this system are obtained with arbitrarily large initial data. Making use of the uniform-in-time bounds for the densities from above and below, exponential decay of weak solution to the unique steady state is obtained without any smallness restriction to the size of the initial data. In particular, our results show that degeneration to single-fluid motion will not occur as long as in the initial distribution both components are present at every point.

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arXiv2018

Homogenization of a non-homogeneous fluid

We consider a non--homogeneous incompressible and heat conducting fluid confined to a 3D domain perforated by tiny holes. The ratio of the diameter of the holes and their mutual distance is critical, the former being equal to $ε^3$, the latter proportional to $ε$, where $ε$ is a small parameter. We identify the asymptotic limit for $ε\to 0$, in which the momentum equation contains a friction term of Brinkman type determined uniquely by the viscosity and geometric properties of the perforation. Besides the inhomogeneity of the fluid, we allow the viscosity and the heat conductivity coefficient to depend on the temperature, where the latter is determined via the Fourier law with homogenized (oscillatory) heat conductivity coefficient that is different for the fluid and the solid holes. To the best of our knowledge, this is the first result in the critical case for the inhomogenous heat--conducting fluid.

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arXiv2017

Global weak solutions to the one-dimensional compressible heat-conductive MHD equations without resistivity

We investigate the initial-boundary value problem for one-dimensional compressible, heat-conductive, non-resistive MHD equations of viscous, ideal polytropic fluids in the Lagrangian coordinates. The existence and Lipschitz continuous dependence on the initial data of global weak solutions are established. Uniqueness of weak solutions follows as a direct consequence of stability.

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arXiv2017

Global weak solutions and long time behavior for 1D compressible MHD equations without resistivity

We study the initial-boundary value problem for 1D compressible MHD equations of viscous non-resistive fluids in the Lagrangian mass coordinates. Based on the estimates of upper and lower bounds of the density, weak solutions are constructed by approximation of global regular solutions, the existence of which has recently been obtained by Jiang and Zhang in [17]. Uniqueness of weak solutions is also proved as a consequence of Lipschitz continuous dependence on the initial data. Furthermore, long time behavior for global solutions is investigated. Specifically, based on the uniform-in-time bounds of the density from above and below away from zero, together with the structure of the equations, we show the exponential decay rate in L^2- and H^1-norm respectively, with initial data of arbitrarily large.

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arXiv2017

Well-posedness of the plasma-vacuum interface problem for ideal incompressible MHD

In this paper, we prove the local well-posedness of plasma-vacuum interface problem for ideal incompressible magnetohydrodynamics under the stability condition: the magnetic field $\mathbf{h}$ and the vacuum magnetic field $\hat{\mathbf{h}}$ are non-collinear on the interface(i.e., $|\mathbf{h}\times \hat{\mathbf{h}}|>0$), which was introduced by Trakhinin as a stability condition for the compressible plasma-vacuum interface problem.

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arXiv2015

On the motion of viscous, compressible and heat-conducting liquids

We consider a system of equations governing the motion of a viscous, compressible, and heat conducting liquid-like fluid, with a general EOS of Mie-Grueneisen type. In addition, we suppose that the viscosity coefficients may decay to zero for large values of the temperature. We show the existence of global-in-time weak solution, derive a relative energy inequality, and compare the weak solutions with strong one emanating from the same initial data - the weak strong uniqueness property.

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arXiv2015

Nonlinear stability of current-vortex sheet to the incompressible MHD equations

In this paper, we solve a long-standing open problem: nonlinear stability of current-vortex sheet in the ideal incompressible Magneto-Hydrodynamics under the linear stability condition. This result gives a first rigorous confirmation of the stabilizing effect of the magnetic field on Kelvin-Helmholtz instability.

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arXiv2010

A Beale-Kato-Majda Blow-up criterion for the 3-D compressible Navier-Stokes equations

We prove a blow-up criterion in terms of the upper bound of the density for the strong solution to the 3-D compressible Navier-Stokes equations. The initial vacuum is allowed. The main ingredient of the proof is \textit{a priori} estimate for an important quantity under the assumption that the density is upper bounded, whose divergence can be viewed as the effective viscous flux.

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