Uniqueness of Solutions to a Gas-Disk Interaction System

Iatcenko, Anton; Sun, Weiran

doi:10.1007/s00205-019-01459-5

Cited by 2 publications

(2 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that we used u(±0, t) = V(t) here. Integrating (18) with respect to t gives (16). By taking the Taylor expansion,…”

Section: Global Existence Theoremmentioning

confidence: 99%

See 1 more Smart Citation

Long-Time Behavior of a Point Mass in a One-Dimensional Viscous Compressible Fluid and Pointwise Estimates of Solutions

Koike

2019

Preprint

View full text Add to dashboard Cite

A. We consider the motion of a point mass in a one-dimensional viscous compressible barotropic fluid. The fluid-point mass system is governed by the barotropic compressible Navier-Stokes equations and Newton's equation of motion. Our main result concerns the long-time behavior of the fluid and the point mass, and it gives pointwise convergence estimates of the volume ratio and the velocity of the fluid to their equilibrium values. As a corollary, it is shown that the velocity V(t) of the point mass satisfies a decay estimate |V(t)| = O(t −3/2 ) -a faster decay compared to t −1/2 known for the motion of a point mass in the viscous Burgers fluid [J. L. Vázquez and E. Zuazua, Comm. Partial Differential Equations 28 (2003), 1705-1738]. The rate −3/2 is essentially related to the compressibility and the nonlinearity. As a consequence, it follows that the point mass is convected only a finite distance as opposed to the viscous Burgers case. The main tool used in the proof is the pointwise estimates of Green's function. It turns out that the understanding of the time-decay properties of the transmitted and reflected waves at the point mass is essential for the proof.2For initial data with certain symmetry, it could happen that h ′ (t) = 0 for all t ≥ 0; see the footnote in Remark 1.3.

show abstract

“…Note that we used u(±0, t) = V(t) here. Integrating (18) with respect to t gives (16). By taking the Taylor expansion,…”

Section: Global Existence Theoremmentioning

confidence: 99%

“…It was started by the work of Caprino, Marchioro and Pulvirenti [5] and extended by various authors. See [16,19] and the references therein.…”

mentioning

confidence: 99%

Long-Time Behavior of a Point Mass in a One-Dimensional Viscous Compressible Fluid and Pointwise Estimates of Solutions

Koike

2019

Preprint

View full text Add to dashboard Cite

show abstract

Long-time behavior of a point mass in a one-dimensional viscous compressible fluid and pointwise estimates of solutions

Koike

2021

Journal of Differential Equations

View full text Add to dashboard Cite

Uniqueness of Solutions to a Gas-Disk Interaction System

Cited by 2 publications

References 13 publications

Long-Time Behavior of a Point Mass in a One-Dimensional Viscous Compressible Fluid and Pointwise Estimates of Solutions

Long-Time Behavior of a Point Mass in a One-Dimensional Viscous Compressible Fluid and Pointwise Estimates of Solutions

Long-time behavior of a point mass in a one-dimensional viscous compressible fluid and pointwise estimates of solutions

Contact Info

Product

Resources

About