Isentropic Approximation¶of the Compressible Euler System¶in One Space Dimension

2000 ◽  
Vol 155 (3) ◽  
pp. 171-199 ◽  
Author(s):  
Laure Saint-Raymond
Keyword(s):  
Space Dimension ◽  
Euler System ◽  
Compressible Euler ◽  
Isentropic Approximation ◽  
One Space Dimension

scholarly journals A counterexample to well-posedness of entropy solutions to the compressible Euler system

2014 ◽  
Vol 11 (03) ◽  
pp. 493-519 ◽  
Author(s):  
Elisabetta Chiodaroli
Keyword(s):  
Space Dimension ◽  
Initial Density ◽  
Euler System ◽  
Entropy Solutions ◽  
Periodic Case ◽  
Time Interval ◽  
Finite Time Interval ◽  
Compressible Euler ◽  
The Cauchy Problem ◽  
Spatially Periodic

We consider entropy solutions to the Cauchy problem for the isentropic compressible Euler equations in the spatially periodic case. In more than one space dimension, the methods developed by De Lellis–Székelyhidi enable us to show here failure of uniqueness on a finite time-interval for entropy solutions starting from any continuously differentiable initial density and suitably constructed bounded initial linear momenta.

scholarly journals Self-adjoint Dirac type Hamiltonians in one space dimension with a mass jump

2015 ◽  
Vol 48 (4) ◽  
pp. 045207 ◽  
Author(s):  
L A González-Díaz ◽  
Alberto A Díaz ◽  
S Díaz-Solórzano ◽  
J R Darias
Keyword(s):  
Space Dimension ◽  
Dirac Type ◽  
One Space Dimension

scholarly journals LOW REGULARITY WELL-POSEDNESS OF THE DIRAC–KLEIN–GORDON EQUATIONS IN ONE SPACE DIMENSION

2008 ◽  
Vol 10 (02) ◽  
pp. 181-194 ◽  
Author(s):  
SIGMUND SELBERG ◽  
ACHENEF TESFAHUN
Keyword(s):  
Dirac Operator ◽  
Space Dimension ◽  
One Dimension ◽  
Well Posedness ◽  
Low Regularity ◽  
Klein Gordon ◽  
One Space Dimension

We extend recent results of Machihara and Pecher on low regularity well-posedness of the Dirac–Klein–Gordon (DKG) system in one dimension. Our proof, like that of Pecher, relies on the null structure of DKG, recently completed by D'Ancona, Foschi and Selberg, but we show that in 1d the argument can be simplified by modifying the choice of projections for the Dirac operator. We also show that the result is best possible up to endpoint cases, if one iterates in Bourgain–Klainerman–Machedon spaces.

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