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Baoquan Yuan

Publications and source records attributed to Baoquan Yuan.

18 recordsLinked to original sources
arXiv2024

Global regularity of 2D Rayleigh-Bénard equations with logarithmic supercritical dissipation

In this paper, we study the global regularity problem for the 2D Rayleigh-Bénard equations with logarithmic supercritical dissipation. By exploiting a combined quantity of the system, the technique of Littlewood-Paley decomposition and Besov spaces, and some commutator estimates, we establish the global regularity of a strong solution to this equations in the Sobolev space $H^{s}(\mathbb{R}^{2})$ for $s \ge2$.

math.AP↗
arXiv2023

Global regularity for the 2D micropolar Rayleigh-Bénard convection system with velocity zero dissipation and temperature critical dissipation

This paper studies the global regularity problem for the 2D micropolar Rayleigh-Bénard convection system with velocity zero dissipation, micro-rotation velocity Laplace dissipation and temperature critical dissipation. By introducing a combined quantity and using the technique of Littlewood-Paley decomposition, we establish the global regularity result of solutions to this system.

math.AP↗
arXiv2023

Global regularity of 2D generalized incompressible magnetohydrodynamic equations

In this paper, we are concerned with the two-dimensional (2D) incompressible magnetohydrodynamic (MHD) equations with velocity dissipation given by $(-Δ)^α$ and magnetic diffusion given by reducing about logarithmic diffusion from standard Laplacian diffusion. More precisely, we establish the global regularity of solutions to the system as long as the power $α$ is a positive constant. In addition, we prove several global \emph{a priori} bounds for the case $α=0$. In particular, our results significantly improve previous works and take us one step closer to a complete resolution of the global regularity issue on the 2D resistive MHD equations, namely, the case when the MHD equations only have standard Laplacian magnetic diffusion.

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arXiv2022

Global large solution for the tropical climate model with diffusion

This paper studies the d-dimensional (d=2,3) tropical climate model with only the dissipation of the first baroclinic model of the velocity ($-ηΔv$). By choosing a class of special initial data $(u_0,v_0,θ_0)$ whose $H^s(\mathbb{R}^d)$ norm can be arbitrarily large, we obtain the global smooth solution of d-dimensional tropical climate model.

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arXiv2021

Global existence of strong solutions to the multi-dimensional inhomogeneous incompressible MHD equations

This paper is concerned with the Cauchy problem of the multi-dimensional incompressible magnetohydrodynamic equations with inhomogeneous density and fractional dissipation. It is shown that when $α+β=1+\frac{n}{2}$ satisfying $1\leq β\leq α\leq\min \{\frac{3β}{2},\frac{n}{2},1+\frac{n}{4}\}$ and $\frac{n}{4}<α$ for $n\geq3$ , then the inhomogeneous incompressible MHD equations has a unique global strong solution for the initial data in Sobolev space which do not need a small condition.

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arXiv2020

Existence and uniqueness of local weak solution of d-dimensional tropical climate model without thermal diffusion in inhomogeneous Besov space

This paper studies the existence and uniqueness of local weak solutions to the d-dimensional tropical climate model without thermal diffusion. We establish that, when $α=β\geq1$, $η=0$, any initial data $(u_{0},v_{0})\in B_{2,1}^{1+\frac{d}{2}-2α}(\mathbb{R}^{d})$ and $θ_{0}\in B_{2,1}^{1+\frac{d}{2}-α}(\mathbb{R}^{d})$ yields a unique weak solution.

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arXiv2020

The global well-posedness of strong solutions to 2D MHD equations in Lei-Lin space

In this paper, we study the Cauchy problem of the 2D incompressible magnetohydrodynamic equations in Lei-Lin space. The global well-posedness of a strong solution in the Lei-Lin space $χ^{-1}(\mathbb{R}^2)$ with any initial data in $χ^{-1}(\mathbb{R}^2)\cap L^2(\mathbb{R}^2)$ is established. Furthermore, the uniqueness of the strong solution in $χ^{-1}(\mathbb{R}^2)$ and the Leray-Hopf weak solution in $L^2(\mathbb{R}^2)$ is proved.

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arXiv2017

Global existence and decay rate of strong solution to incompressible Oldroyd type model equations

This paper investigates the global existence and the decay rate in time of a solution to the Cauchy problem for an incompressible Oldroyd model with a deformation tensor damping term. There are three major results. The first is the global existence of the solution for small initial data. Second, we derive the sharp time decay of the solution in $L^{2}-$norm. Finally, the sharp time decay of the solution of higher order Sobolev norms is obtained.

math.AP↗
arXiv2016

Global Regularity of 2D almost resistive MHD Equations

Whether or not the solution to 2D resistive MHD equations is globally smooth remains open. This paper establishes the global regularity of solutions to the 2D almost resistive MHD equations, which require the dissipative operators $\mathcal{L}$ weaker than any power of the fractional Laplacian. The result is an improvement of the one of Fan et al. (Global Cauchy problem of 2D generalized MHD equations, Monatsh. Math., 175 (2014), pp. 127-131) which ask for $α>0, β=1$.

math.AP↗
arXiv2013

The 2D Incompressible Magnetohydrodynamics Equations with only Magnetic Diffusion

This paper examines the global (in time) regularity of classical solutions to the 2D incompressible magnetohydrodynamics (MHD) equations with only magnetic diffusion. Here the magnetic diffusion is given by the fractional Laplacian operator $(-Δ)^β$. We establish the global regularity for the case when $β>1$. This result significantly improves previous work which requires $β>\frac32$ and brings us closer to the resolution of the well-known global regularity problem on the 2D MHD equations with standard Laplacian magnetic diffusion, namely the case when $β=1$.

math.AP↗
arXiv2013

Remarks on global regularity of 2D generalized MHD equations

In this paper, we investigate the global regularity of 2D generalized MHD equations, in which the dissipation term and magnetic diffusion term are $ν(-Δ)^αu$ and $η(-Δ)^βb$ respectively. Let $(u_{0}, b_{0})\in H^{s}$ with $s\geq2$, it is showed that the smooth solution $(u(x,t),b(x,t))$ is globally regular for the case $ 0\leqα\leq\{1}{2}, α+β> \{3}{2}$.

math.AP↗
arXiv2009

On the regularity criteria of weak solutions to the micropolar fluid equations in Lorentz space

In this paper the regularity of weak solutions and the blow-up criteria of smooth solutions to the micropolar fluid equations on three dimension space are studied in the Lorentz space $L^{p,\infty}(\mathbb{R}^3)$. We obtain that if $u\in L^q(0,T;L^{p,\infty}(\mathbb{R}^3))$ for $\frac2q+\frac3p\le 1$ with $3<p\le \infty$; or $\nabla u\in L^q(0,T;L^{p,\infty}(\mathbb{R}^3))$ for $\frac2q+\frac3p\le 2$ with $\frac32<p\le \infty$; or the pressure $P\in L^q(0,T;L^{p,\infty}(\mathbb{R}^3))$ for $\frac2q+\frac3p\le 2$ with $\frac32<p\le \infty$; or $\nabla P\in L^q(0,T;L^{p,\infty}(\mathbb{R}^3))$ for $\frac2q+\frac3p\le 3$ with $1<p\le \infty$, then the weak solution $(u,ω)$ satisfying the energy inequality is a smooth solution on $[0,T)$.

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arXiv2008

On well-posedness of the Cauchy problem for MHD system in Besov spaces

This paper is devoted to the study of the Cauchy problem of incompressible magneto-hydrodynamics system in framework of Besov spaces. In the case of spatial dimension $n\ge 3$ we establish the global well-posedness of the Cauchy problem of incompressible magneto-hydrodynamics system for small data and the local one for large data in Besov space $\dot{B}^{\frac np-1}_{p,r}(\mr^n)$, $1\le p<\infty$ and $1\le r\le\infty$. Meanwhile, we also prove the weak-strong uniqueness of solutions with data in $\dot{B}^{\frac np-1}_{p,r}(\mr^n)\cap L^2(\mr^n)$ for $\frac n{2p}+\frac2r>1$. In case of $n=2$, we establish the global well-posedness of solutions for large initial data in homogeneous Besov space $\dot{B}^{\frac2p-1}_{p,r}(\mr^2)$ for $2< p<\infty$ and $1\le r<\infty$.

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arXiv2006

Well-posedness of the Cauchy problem for the fractional power dissipative equations

This paper studies the Cauchy problem for the nonlinear fractional power dissipative equation $u_t+(-\triangle)^αu= F(u)$ for initial data in the Lebesgue space $L^r(\mr^n)$ with $\ds r\ge r_d\triangleq{nb}/({2α-d})$ or the homogeneous Besov space $\ds\dot{B}^{-σ}_{p,\infty}(\mr^n)$ with $\dsσ=(2α-d)/b-n/p$ and $1\le p\le \infty$, where $α>0$, $F(u)=f(u)$ or $Q(D)f(u)$ with $Q(D)$ being a homogeneous pseudo-differential operator of order $d\in[0,2α)$ and $f(u)$ is a function of $u$ which behaves like $|u|^bu$ with $b>0$.

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