Blow-up phenomena for compressible Euler equations with non-vacuum initial data

Wong, Sen; Yuen, Manwai

doi:10.1007/s00033-015-0535-9

Cited by 18 publications

(6 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this paper, we are interested in the blowup of classical solutions to the Cauchy problem (‐). There are huge literatures on the blow‐up results for the compressible Euler equations and compressible Navier‐Stokes equations, but the blow‐up results for the coupled kinetic‐fluid equations are very few because the kinetic and fluid equations have different characteristic curves; see Choi . Very recently, Choi deals with the finite‐time blow‐up phenomena of classical solutions for Vlasov/Navier‐Stokes equations under suitable assumptions on the initial configurations.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Blowup of classical solutions to the pressureless Euler/isentropic Navier‐Stokes equations

Dong

Lou

Yang

2019

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, we will show the blowup of classical solutions to the Cauchy problem for the pressureless Euler/isentropic Navier-Stokes equations in arbitrary dimensions under some restrictions on the initial data. Compared with the degenerate viscosities appeared in the recent work, we consider the constant viscosities, but we can remove the condition that the adiabatic exponent has a upper bound, which was a key constraint in the proof of the blow-up result is based on the construction of some new differential inequalities.

show abstract

Section: Introduction and Main Resultsmentioning

confidence: 99%

Blowup of classical solutions to the pressureless Euler/isentropic Navier‐Stokes equations

Dong

Lou

Yang

2019

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…If ρ 0 (x) > 0 for all x 2 R N , then ρ(t, x) > 0 " t ≥ 0 and " x 2 R N . 35 Here the numerical mR scheme is used to solve one-dimensional isothermal Euler equations of gas dynamics. Actually, the Rusanov's method is a local Lax-Friedrichs method that one seeks a local maximum rather than a global maximum of the wave speed, which is illustrated.…”

Section: Introductionmentioning

confidence: 99%

Simulating isothermal Euler model with non-vacuum initial data via mR scheme

Abdelrahman

Alkhidhr

Mohamed

2022

Journal of Low Frequency Noise, Vibration and Active Control

View full text Add to dashboard Cite

We consider the isothermal Euler model with non-vacuum initial data. We extract the Riemann invariants of the isothermal Euler model, which admits vital applications. We also design the modified Rusanov (mR) scheme to solve the isothermal Euler model. This scheme consists of two steps, the first step of the scheme depends on a local parameter allowing to control diffusion. The second stage recovers conservation equation. This technique is a straightforward to implement and precise. We compare this scheme with the Rusanov scheme via three numerical examples. This numerical study verifies the efficiency of the mR scheme. Finally, the mR scheme can be used to solve many other models in applied science.

show abstract

“…It is well known that 3D compressible Euler equations will develop singularities if the initial data are compressed and outgoing . Moreover, the finite time blow‐up phenomena is regardless of the size of initial disturbance .…”

Section: Introductionmentioning

confidence: 99%

Global existence of classical solutions for the 3D generalized compressible Oldroyd‐B model

Zhu

2020

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, we prove the global existence of small classical solutions to the 3D generalized compressible Oldroyd‐B system. It can be seen as compressible Euler equations coupling the evolution of stress tensor τ. The result mainly shows that singularity of solutions to compressible Euler equations can be prevented by the coupling of viscoelastic stress tensor. Moreover, unlike most complex fluids containing compressible Euler equations, the irrotational condition ∇×u=0 would not be proposed here to achieve the global well‐posedness.

show abstract

Blow-up phenomena for compressible Euler equations with non-vacuum initial data

Cited by 18 publications

References 14 publications

Blowup of classical solutions to the pressureless Euler/isentropic Navier‐Stokes equations

Blowup of classical solutions to the pressureless Euler/isentropic Navier‐Stokes equations

Simulating isothermal Euler model with non-vacuum initial data via mR scheme

Global existence of classical solutions for the 3D generalized compressible Oldroyd‐B model

Contact Info

Product

Resources

About