The Dissipative Terms in the Hydrodynamic Equations 13

2018 ◽  
pp. 63-66
Author(s):  
I.M. Khalatnikov
Keyword(s):  
Hydrodynamic Equations ◽  
Dissipative Terms

The elasto-hydrodynamic equations of the colloidal crystals

1988 ◽  
Vol 49 (7) ◽  
pp. 1119-1125 ◽  
Author(s):  
M. Jorand ◽  
E. Dubois-Violette ◽  
B. Pansu ◽  
F. Rothen
Keyword(s):  
Colloidal Crystals ◽  
Hydrodynamic Equations

The motion of the particles volume corresponding to invariant solution of rank 2 submodel of hydrodynamic type

2016 ◽  
Vol 11 (2) ◽  
pp. 205-209
Author(s):  
D.T. Siraeva
Keyword(s):  
Equation Of State ◽  
Invariant Solution ◽  
Hydrodynamic Type ◽  
Lagrangian Coordinates ◽  
Hydrodynamic Equations ◽  
Rank 2 ◽  
Invariant Submodel ◽  
Entropy Functions

Invariant submodel of rank 2 on the subalgebra consisting of the sum of transfers for hydrodynamic equations with the equation of state in the form of pressure as the sum of density and entropy functions, is presented. In terms of the Lagrangian coordinates from condition of nonhyperbolic submodel solutions depending on the four essential constants are obtained. For simplicity, we consider the solution depending on two constants. The trajectory of particles motion, the motion of parallelepiped of the same particles are studied using the Maple.

Classical Kinetic Theory

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Kinetic Equation ◽  
Equation Of State ◽  
Mean Field ◽  
Ideal Gas ◽  
Hydrodynamic Equations ◽  
Free Particles ◽  
Internal Mechanism ◽  
The Mean ◽  
Energy Gains ◽  
Non Locality

The classical non-ideal gas shows that the two original concepts of the pressure based of the motion and the forces have eventually developed into drift and dissipation contributions. Collisions of realistic particles are nonlocal and non-instant. A collision delay characterizes the effective duration of collisions, and three displacements, describe its effective non-locality. Consequently, the scattering integral of kinetic equation is nonlocal and non-instant. The non-instant and nonlocal corrections to the scattering integral directly result in the virial corrections to the equation of state. The interaction of particles via long-range potential tails is approximated by a mean field which acts as an external field. The effect of the mean field on free particles is covered by the momentum drift. The effect of the mean field on the colliding pairs causes the momentum and the energy gains which enter the scattering integral and lead to an internal mechanism of energy conversion. The entropy production is shown and the nonequilibrium hydrodynamic equations are derived. Two concepts of quasiparticle, the spectral and the variational one, are explored with the help of the virial of forces.

scholarly journals Global small data solutions for semilinear waves with two dissipative terms

2021 ◽  
Author(s):  
Wenhui Chen ◽  
Marcello D’Abbicco ◽  
Giovanni Girardi
Keyword(s):  
Wave Equations ◽  
Space Dimension ◽  
Full Range ◽  
Small Data ◽  
Decay Estimates ◽  
Time Decay ◽  
Nonexistence Result ◽  
Derivative Type ◽  
Long Time ◽  
Dissipative Terms

AbstractIn this work, we prove the existence of global (in time) small data solutions for wave equations with two dissipative terms and with power nonlinearity $$|u|^p$$ | u | p or nonlinearity of derivative type $$|u_t|^p$$ | u t | p , in any space dimension $$n\geqslant 1$$ n ⩾ 1 , for supercritical powers $$p>{\bar{p}}$$ p > p ¯ . The presence of two dissipative terms strongly influences the nature of the problem, allowing us to derive $$L^r-L^q$$ L r - L q long time decay estimates for the solution in the full range $$1\leqslant r\leqslant q\leqslant \infty $$ 1 ⩽ r ⩽ q ⩽ ∞ . The optimality of the critical exponents is guaranteed by a nonexistence result for subcritical powers $$p<{\bar{p}}$$ p < p ¯ .

Wave propagation in the presence of a spatially uniform external periodic magnetic field in two-temperature plasma

1982 ◽  
Vol 28 (1) ◽  
pp. 93-101
Author(s):  
Sanjay Kumar Ghosh
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Fluid Model ◽  
Hydrodynamic Equations ◽  
Temperature Plasma ◽  
Uniform External Magnetic Field ◽  
Two Fluid Model ◽  
Excitation Conditions ◽  
Two Fluid ◽  
Two Temperature

Starting from the two-fluid model hydrodynamic equations, a dispersion relation is obtained for wave propagation through a two-temperature plasma perpendicular to the direction of the spatially uniform external magnetic field B0cosω0t and several excitation conditions are deduced.

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