scholarly journals Double asymptotic expansion of the resolving operator of the cauchy problem for the line-arized system of gas dynamics

2019 ◽  
Vol 484 (2) ◽  
pp. 134-137
Author(s):  
A. I. Allilueva ◽  
A. I. Shafarevich
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Expansion ◽  
Gas Dynamics ◽  
Acoustic Modes ◽  
Small Viscosity ◽  
The Cauchy Problem ◽  
Linearized System

We obtain double asymptotic expansion (with respect to smoothness and small viscosity) of the resolving operator of the Cauchy problem for the linearized system of gas dynamics. We derive estimates for the summands and for the residual in the Sobolev scale.We describe explicitly hydrodynamic and acoustic modes.

The Cauchy problem for the system of Zakharov equations arising from ion-acoustic modes

1996 ◽  
Vol 126 (4) ◽  
pp. 811-820 ◽  
Author(s):  
Guo Boling ◽  
Yuan Guangwei
Keyword(s):  
Cauchy Problem ◽  
Initial Value Problem ◽  
Existence And Uniqueness ◽  
A Priori ◽  
Cauchy Data ◽  
Continuous Method ◽  
Initial Value ◽  
Acoustic Modes ◽  
Ion Acoustic ◽  
The Cauchy Problem

In this paper the initial value problem for a class of Zakharov equations arising from ion-acoustic modes is discussed. Without assuming the Cauchy data are small, we prove the existence and uniqueness of the global smooth solution for the problem via the so-called continuous method and delicate a priori estimates.

The global Hölder-continuous solution of isentropic gas dynamics

1993 ◽  
Vol 123 (2) ◽  
pp. 231-238 ◽  
Author(s):  
Yun-Guang Lu
Keyword(s):  
Cauchy Problem ◽  
Gas Dynamics ◽  
Continuous Solution ◽  
Hölder Continuous ◽  
Vanishing Viscosity ◽  
Equations Of Gas Dynamics ◽  
The Cauchy Problem ◽  
Isentropic Gas Dynamics ◽  
Isentropic Gas

SynopsisThis paper considers the Cauchy problem for the isentropic equations of gas dynamics in Euler coordinates ρt + (ρu)x = 0, (ρu)t + (ρu)2 + P(ρ))x=0 and gives the Hölder-continuous solution by applying the method of vanishing viscosity.

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO DRIFT-DIFFUSION SYSTEM WITH GENERALIZED DISSIPATION

2009 ◽  
Vol 19 (06) ◽  
pp. 939-967 ◽  
Author(s):  
TAKAYOSHI OGAWA ◽  
MASAKAZU YAMAMOTO
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Asymptotic Expansion ◽  
Initial Data ◽  
Global Existence ◽  
Asymptotic Behavior Of Solutions ◽  
Large Initial Data ◽  
Drift Diffusion ◽  
Nonlinear Parabolic ◽  
The Cauchy Problem

We show the global existence and asymptotic behavior of solutions for the Cauchy problem of a nonlinear parabolic and elliptic system arising from semiconductor model. Our system has generalized dissipation given by a fractional order of the Laplacian. It is shown that the time global existence and decay of the solutions to the equation with large initial data. We also show the asymptotic expansion of the solution up to the second terms as t → ∞.

scholarly journals On the Sharp Gårding Inequality for Operators with Polynomially Bounded and Gevrey Regular Symbols

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1938
Author(s):  
Alexandre Arias Junior ◽  
Marco Cappiello
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Expansion ◽  
Evolution Equations ◽  
Gevrey Estimates ◽  
The Cauchy Problem ◽  
Precise Expression

In this paper, we analyze the Friedrichs part of an operator with polynomially bounded symbol. Namely, we derive a precise expression of its asymptotic expansion. In the case of symbols satisfying Gevrey estimates, we also estimate precisely the regularity of the terms in the asymptotic expansion. These results allow new and refined applications of the sharp Gårding inequality in the study of the Cauchy problem for p-evolution equations.

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