arXiv subjects

Qianfeng Li

Publications and source records attributed to Qianfeng Li.

5 recordsLinked to original sources

arXiv2026

An Inverse Problem for Determining the Piston Speed from a Given Lipschitz Leading Shock

We analyze an inverse problem for determining the piston speed and the associated flow field from a prescribed leading shock and the initial data in a shock tube. The gas flow is described by the isentropic Euler equations (i.e., the $p$-system), while the trajectory of the leading shock is prescribed as a given Lipschitz curve. Under an Ole\u{i}nik-type entropy condition on the leading shock, we develop a modified wavefront tracking scheme to construct the flow field behind the shock. This construction enables us to determine the corresponding piston speed and the associated flow field.

math.AP↗

arXiv2026

Weak-Strong Uniqueness for a Rigid Body Immersed in an Inviscid Compressible Fluid

We consider the coupled motion of a free rigid body immersed in an inviscid compressible isentropic fluid. By means of a vanishing viscosity limit, we obtain the local-in-time existence of a dissipative measure-valued solution to the model. Moreover, we establish the weak-strong uniqueness property of the obtained measure-valued solution. To our knowledge, this is the first mathematical result on compressible inviscid fluid-structure interaction. The key novel technique is the construction of a suitable approximation of the test function in the weak formulation of the inviscid system, as the space of test functions depends on the viscosity parameter.

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arXiv2025

On the one-dimensional piston model with Large Velocity Variations

This paper investigates the dynamics of a one-dimensional piston expanding into a static rarefied gas. Using asymptotic analysis in the limit of vanishing initial density, we derive sharp estimates for the piston-shock distance, the separation of characteristic speeds, and the reflection coefficient associated with characteristic waves interacting with the leading shock front. Based on these estimates, we apply the method of characteristics to prove the global-in-time existence of piecewise smooth solutions. The resulting flow structure exhibits significant velocity variations. The analysis reveals a stable mechanism that operates in the vanishing-density limit of the piston model.

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arXiv2025

An Inverse Problem for Multi-Dimensional Piston Models with Large Velocity Variations

When a circular symmetric piston suddenly expands into a still gas, a leading shock wave is generated. This paper investigates an inverse problem of reconstructing the trajectory of the piston from the given leading shock front and the given initial flow conditions. We observe that in piston models, as the initial density goes to zero, the piston approaches the shock front; however, in the region between the piston and the shock front, the strict hyperbolicity of the system degenerates. By applying asymptotic analysis, we provide quantitative characterizations of the distance between the piston and the shock front, and the degeneration of strict hyperbolicity. Consequently, by designing appropriate a priori assumptions to balance the benefits and drawbacks arising as the initial density approaches zero, we employ the method of characteristics to prove the global-in-time existence of the piecewise smooth solution for this inverse problem. In particular, the resulting flow structure exhibits significant velocity variations.

math.AP↗

arXiv2024

Hypersonic limit for steady compressible Euler flows passing straight cones

We investigate the hypersonic limit for steady, uniform, and compressible polytropic gas passing a symmetric straight cone. By considering Radon measure solutions, we show that as the Mach number of the upstream flow tends to infinity, the measures associated with the weak entropy solution containing an attached shock ahead of the cone converge vaguely to the measures associated with a Radon measure solution to the conical hypersonic-limit flow. This justifies the Newtonian sine-squared pressure law for cones in hypersonic aerodynamics. For Chaplygin gas, assuming that the Mach number of the incoming flow is less than a finite critical value, we demonstrate that the vertex angle of the leading shock is independent of the conical body's vertex angle and is totally determined by the incoming flow's Mach number. If the Mach number exceeds the critical value, we explicitly construct a Radon measure solution with a concentration boundary layer.

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