On the conditions for the breaking of oscillations in a cold plasma

Rozanova, Olga; Chizhonkov, E. V.

doi:10.1007/s00033-020-01440-3

Cited by 33 publications

(50 citation statements)

References 15 publications

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“…with F (G) found from (12) or (13), where the constant C d in (12) or (13) does not depend on the initial point r 0 and the periods of oscillations given as (15) are equal for all characteristics. If we fix C d , we obtain the relation between G and F in this special kind of solution, and the corresponding initial data.…”

Section: Simple Wavesmentioning

confidence: 92%

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On the behavior of multidimensional axisymmetric solutions of the repulsive Euler-Poisson equations

Rozanova¹

2022

Preprint

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Section: Simple Wavesmentioning

confidence: 92%

“…It is not surprising that there exists a special subclass of solutions to (6) equations that have a more regular behavior than solutions in the general case. For one-dimensional equations of relativistic cold plasma considered in [15] the situation is similar, i.e. simple waves can be globally smooth in time.…”

Section: Simple Wavesmentioning

confidence: 99%

On the behavior of multidimensional axisymmetric solutions of the repulsive Euler-Poisson equations

Rozanova¹

2022

Preprint

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“…We eliminate Ξ from ( 7) using (8) and denote for convenience s = λ − 1 ≤ 0 (the inequality follows from (3), since n ≥ 0). Thus, we get…”

Section: Sufficient Conditions For Boundedness Of Densitymentioning

confidence: 99%

“…Such a system has been considered in [8], where the following criterion for the preservation of the global in time smoothness was obtained: at each point x 0 ∈ R (here x = x 1 ) the condition…”

Section: Particular Casesmentioning

confidence: 99%

On the properties of multidimensional electrostatic oscillations of an electron plasma

Rozanova¹

2022

Preprint

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We consider the classical Cauchy problem for a system of equations describing 3D arbitrary electrostatic oscillations of the cold plasma and find a sufficient condition guaranteeing the boundedness of density during the first period of oscillations. Moreover, we introduce an iteration procedure that allows estimating the blow-up time from below. We also consider examples of electrostatic oscillations in one, two, and three dimensions. For the particular case of two-dimensional initial data with axial symmetry, refined sufficient conditions for destruction and preservation of smoothness in the first period of oscillations are obtained.

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“…The relation W (θ) = P (θ)Q −1 (θ) implies that the derivatives of the solution to the Cauchy problem ( 7), ( 8) go to infinity in a finite time along the characteristic starting from the point ρ 0 ∈ R if and only if there is θ * > 0 such that Q(θ * , ρ 0 = 0. The smallest root θ * > 0 over all ρ 0 ∈ R corresponds to the blow up time (15).…”

Section: A Criterion Of the Singularity Formationmentioning

confidence: 99%

The Interplay of Regularizing Factors in the Model of Upper Hybrid Oscillations of Cold Plasma

Delova¹,

Rozanova²

2021

Preprint

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A one-dimensional nonlinear model of the so-called upper hybrid oscillations in a magnetoactive plasma is investigated taking into account electron-ion collisions. It is known that both the presence of an external magnetic field of strength B 0 and a sufficiently large collisional factor ν help suppress the formation of a finite-dimensional singularity in a solution (breaking of oscillations). Nevertheless, the suppression mechanism is different: an external magnetic field increases the oscillation frequency, and collisions tend to stabilize the medium and suppress oscillations. In terms of the initial data and the coefficients B 0 and ν, we establish a criterion for maintaining the global smoothness of the solution. Namely, for fixed B 0 and ν ≥ 0 one can precisely divide the initial data into two classes: one leads to stabilization to the equilibrium, and the other leads to the destruction of the solution in a finite time.Next, we examine the nature of the stabilization. We show that for small |B 0 | an increase in the intensity factor first leads to a change in the oscillatory behavior of the solution to monotonic damping, which is then again replaced by oscillatory damping. At large values of |B 0 |, the solution is characterized by oscillatory damping regardless of the value of the intensity factor ν.

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On the conditions for the breaking of oscillations in a cold plasma

Cited by 33 publications

References 15 publications

On the behavior of multidimensional axisymmetric solutions of the repulsive Euler-Poisson equations

On the behavior of multidimensional axisymmetric solutions of the repulsive Euler-Poisson equations

On the properties of multidimensional electrostatic oscillations of an electron plasma

The Interplay of Regularizing Factors in the Model of Upper Hybrid Oscillations of Cold Plasma

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