arXiv subjects

Yaobin Ou

Publications and source records attributed to Yaobin Ou.

7 recordsLinked to original sources

arXiv2026

The anelastic approximation and convergence rate for the compressible Navier-Stokes equations with ill-prepared data in bounded domains

We justify the anelastic approximation and establish a convergence rate for local strong solutions to the isentropic compressible Navier-Stokes equations in a three-dimensional bounded domain, with ill-prepared initial data and vorticity-slip boundary conditions. When the Mach and Froude numbers vanish at the same rate $ε$, the system converges to an anelastic system with nonconstant hydrostatic density. Compared with the incompressible limit, the balance between singular pressure and gravity generates a variable-coefficient acoustic operator and additional commutators. To overcome these difficulties, we introduce the pressure perturbation adapted to the hydrostatic balance and establish weighted acoustic and vorticity estimates, yielding uniform-in-$ε$ estimates. We then use the weighted Helmholtz decomposition and time-averaging technique to prove the strong convergence of solenoidal component of the momentum and obtain an error bound controlled by $ε$ and the initial error in the projected momentum. Our analysis reveals the weighted cancellation mechanism that applies to singular limits around a class of nonconstant equilibria.

math.AP↗

arXiv2026

Low Mach number limit of the full Navier-Stokes equations with no-slip boundary conditions and large temperature variations

In this paper, we rigorously justify the low Mach number limit of the full compressible Navier-Stokes equations in a three-dimensional smooth bounded domain, subject to the no-slip boundary condition for the velocity and well-prepared initial data. In the presence of heat conduction and large temperature variations, we establish the uniform estimates for strong solutions on a time interval independent of the Mach number by constructing an energy functional in a Sobolev framework. The no-slip boundary condition cannot provide the vorticity boundary relation used in the slip-boundary setting. To overcome this difficulty, a divergence-free Stokes lifting of the boundary trace for the time derivative of the modified velocity is employed to define a test function vanishing on the boundary, which enables the transfer of a priori estimates from the velocity to the temperature.

math.AP↗

arXiv2023

Low Mach number limit for non-isentropic magnetohydrodynamic equations with ill-prepared data and zero magnetic diffusivity in bounded domains

In this article, we verify the low Mach number limit of strong solutions to the non-isentropic compressible magnetohydrodynamic equations with zero magnetic diffusivity and ill-prepared initial data in three-dimensional bounded domains, when the density and the temperature vary around constant states. Invoking a new weighted energy functional, we establish the uniform estimates with respect to the Mach number, especially for the spatial derivatives of high order. Due to the vorticity-slip boundary condition of the velocity, we decompose the uniform estimates into the part for the fast variables and the other one for the slow variables. In particular, the weighted estimates of highest-order spatial derivatives of the fast variables are crucial for the uniform bounds. Finally, the low Mach number limit is justified by the strong convergence of the density and the temperature, the divergence-free component of the velocity, and the weak convergence of other variables. The methods in this paper can be applied to singular limits of general hydrodynamic equations of hyperbolic-parabolic type, including the full Navier-Stokes equations.

math.AP↗

arXiv2020

Low Mach and low Froude number limit for vacuum free boundary problem of all-time classical solutions of 1-D compressible Navier-Stokes equations

In this paper, we study the low Mach and Froude number limit for the all-time classical solution of a fluid-vacuum free boundary problem of one-dimensional compressible Navier-Stokes equations. No smallness of initial data for the existence of all-time solutions are supposed. The uniform estimates of solutions with respect to the Mach number and the Froude number are established for all the time, in particular for high order derivatives of the pressure, which is a novelty in contrast to previous results. The cases of "ill-prepared" initial data and "well-prepared" initial data are both discussed. It is interesting to see, either both the Mach number and the Froude number vanish, or the time goes to infinity, the limiting functions are the same, that is, the steady state. The main difficulty is that, the system is degenerate near the free boundary and contains singular terms. This result can be viewed as the first one on the low Mach and Froude numbers limit for free boundary problems. At the same time, we also establish the all-time existence of the classical solution with sharp convergent rates to the steady state, while previous results are only concerned with the weak or strong solutions.

math.AP↗

arXiv2013

Incompressible limit of strong solutions to 3-D Navier-Stokes equations with Navier's slip boundary condition for all time

This paper studies the incompressible limit of global strong solutions to the three-dimensional compressible Navier-Stokes equations associated with Navier's slip boundary condition, provided that the time derivatives, up to first order, of solutions are bounded initially. The main idea is to derive a differential inequality with decay, so that the estimates are bounded uniformly both in the Mach number 0<ε<=ε0 for some ε0>0 and the time t>=0.

math.AP↗

arXiv2011

Spherically symmetric solutions to a model for phase transitions driven by configurational forces

We prove the global in time existence of spherically symmetric solutions to an initial-boundary value problem for a system of partial differential equations, which consists of the equations of linear elasticity and a nonlinear, non-uniformly parabolic equation of second order. The problem models the behavior in time of materials in which martensitic phase transitions, driven by configurational forces, take place, and can be considered to be a regularization of the corresponding sharp interface model. By assuming that the solutions are spherically symmetric, we reduce the original multidimensional problem to the one in one space dimension, then prove the existence of spherically symmetric solutions. Our proof is valid due to the essential feature that the reduced problem is one space dimensional.

math.DS↗

arXiv2010

A blow-up criterion for compressible viscous heat-conductive flows

We study an initial boundary value problem for the Navier-Stokes equations of compressible viscous heat-conductive fluids in a 2-D periodic domain or the unit square domain. We establish a blow-up criterion for the local strong solutions in terms of the gradient of the velocity only, which coincides with the famous Beale-Kato-Majda criterion for ideal incompressible flows.

math.AP↗