Remarks on the preceding paper by M. Ben-Artzi ?Global solutions of two-dimensional Navier-Stokes and Euler equations?

1994 ◽  
Vol 128 (4) ◽  
pp. 359-360 ◽  
Author(s):  
Ha�m Brezis
Keyword(s):  
Euler Equations ◽  
Preceding Paper ◽  
Global Solutions ◽  
Navier Stokes ◽  
Two Dimensional

scholarly journals Riemann problem with delta initial data for the two-dimensional steady pressureless isentropic relativistic Euler equations

2021 ◽  
Author(s):  
Yu Zhang ◽  
Yanyan Zhang
Keyword(s):  
Initial Data ◽  
Euler Equations ◽  
Riemann Problem ◽  
Contact Discontinuity ◽  
Global Solutions ◽  
Two Dimensional ◽  
Relativistic Euler Equations ◽  
Riemann Solutions ◽  
Isentropic Relativistic Euler Equations ◽  
The Stability

The Riemann problem for the two-dimensional steady pressureless isentropic relativistic Euler equations with delta initial data is studied. First, the perturbed Riemann problem with three pieces constant initial data is solved. Then, via discussing the limits of solutions to the perturbed Riemann problem, the global solutions of Riemann problem with delta initial data are completely constructed under the stability theory of weak solutions. Interestingly, the delta contact discontinuity is found in the Riemann solutions of the two-dimensional steady pressureless isentropic relativistic Euler equations with delta initial data.

On asymptotic stability of global solutions in the weak L2 space for the two-dimensional Navier–Stokes equations

Analysis ◽  
2015 ◽  
Vol 35 (4) ◽  
Author(s):  
Yasunori Maekawa
Keyword(s):  
Asymptotic Stability ◽  
Stokes Equations ◽  
Global Solutions ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations

AbstractIn this paper we prove the asymptotic stability of small global solutions in the weak

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