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Xiaoguang You

Publications and source records attributed to Xiaoguang You.

7 recordsLinked to original sources
arXiv2026

A small rigid body immersed in a three-dimensional viscous fluid and the vanishing viscosity limit

In this paper, we investigate the asymptotic behavior of a coupled fluid--rigid body system, consisting of a rigid body immersed in a three-dimensional viscous incompressible fluid, as the body size and the fluid viscosity vanish. We prove that the limiting velocity field is governed by the whole-space incompressible Euler equations. Moreover, the influence of the fluid on the rigid body motion is shown to vanish in this limit.

math.AP↗
arXiv2026

Steady Euler flows with contact discontinuities in infinitely long nozzles with general upstream data

We investigate steady compressible Euler flows in two-dimensional infinitely long nozzles, where the piecewise smooth upstream data at infinity admits a characteristic discontinuity. Except the subsonicity condition, no additional constraints are imposed on the data. We establish the existence and uniqueness of subsonic weak solutions associated with a smooth contact discontinuity curve. The original problem is reformulated into an elliptic equation in divergence form with discontinuous coefficients, such that the contact discontinuity conditions are inherently preserved in the solution of the elliptic problem. We further investigate the downstream asymptotic behavior and show that the convergence rate of the flow matches that of the nozzle walls.

math.AP↗
arXiv2026

Global well-posedness of solutions for the equations modelling the motion of a rigid body in a bidimensional perfect fluid

This paper considers a system modelling the evolution of a rigid body immersed in a bidimensional incompressible perfect fluid. In the special case of a disk-shaped rigid body, it was shown by C. Rosier and L. Rosier (2009) that the system admits a unique global solution when the initial fluid velocity $u_0$ belongs to $H^s$ ($s \ge 3$) and its vorticity $\operatorname{curl} u_0$ lies in $L^p$ with $1 \le p < 2$. By establishing a Beale-Kato-Majda type bound, we generalize the result by removing the constraint $\operatorname{curl} u_0 \in L^p$ and allowing the rigid body to be of arbitrary shape. Moreover, we obtain an explicit energy bound.

math.AP↗
arXiv2021

Global Well-Posedness of 2D Second Grade Fluid Equations in Exterior Domain

In this article, we consider 2D second grade fluid equations in exterior domain with Dirichlet boundary conditions. For initial data $\boldsymbol{u}_0 \in \boldsymbol{H}^3(Ω)$, the system is shown to be global well-posed. Furthermore, for arbitrary $T > 0$ and $s \geq 3$, we prove that the solution belongs to $L^\infty([0, T]; \boldsymbol{H}^s(Ω))$ provided that $\boldsymbol{u}_0$ is in $\boldsymbol{H}^s(Ω)$.

math.AP↗
arXiv2021

Singular limit of 2D second grade fluid past an obstacle

In this paper, we consider the 2D second grade fluid past an obstacle satisfying the standard non-slip boundary condition at the surface of the obstacle. Second grade fluid model is a well-known non-Newtonian model, with two parameters: $α$ representing length-scale, while $ν> 0$ corresponding to viscosity. We prove that, under the constraint condition $ν= {o}(α^\frac{4}{3})$, the second grade fluid with a suitable initial velocity converges to the Euler fluid as $α$ tends to zero. Moreover, we estimate the convergence rate of the solution of second grade fluid equations to the one of Euler fluid equations as $ν$ and $α$ approach zero.

math.AP↗
arXiv2021

Global Well-Posedness of 2D Euler-$α$ Equations in Exterior Domain

After casting Euler-$α$ equations into vorticity-stream function formula, we obtain some very useful estimates from the properties of the vorticity formula in exterior domain. Basing on these estimates, one can have got the global existence and uniqueness of the solutions to Euler-$α$ equations in 2D exterior domain provided that the initial data is regular enough.

math.AP↗