Global Lp-properties for the spatially homogeneous Boltzmann equation

Gustafsson, Tommy

doi:10.1007/bf00292919

Cited by 63 publications

(29 citation statements)

References 10 publications

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“…Estimates as given in the following theorem have also been proven in [Gu1], [Gu2] and [MV,Section 2] for kernels with angular cutoff. To our knowledge, the proof presented here is the most elementary one.…”

Section: The Gain Part Of the Collision Operatormentioning

confidence: 84%

“…This investigation started in [Ar], [Gu1] and [Gu2] in the setting of weighted Lebesgue spaces for kernels with angular or Grad's cutoff condition.…”

Section: Remark 11 For the Study Of The Bilinear Operator It Is Commonmentioning

confidence: 99%

“…(see e.g. [Gu1], [Gu2] and [MV]) to impose angular cutoff conditions on b λ (µ). By this, we mean that both frontal and grazing collisions are neglected:…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On Estimates of the Boltzmann Collision Operator with Cut-off

Duduchava

Kirsch

Rjasanow

2005

J. math. fluid mech.

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We present new estimates of the Boltzmann collision operator in weighted Lebesgue and Bessel potential spaces. The main focus is put on hard potentials under the assumption that the angular part of the collision kernel fulfills some weighted integrability condition. In addition, the proofs for some previously known L pestimates have been considerably shortened and carried out by elementary methods. For a class of metric spaces, the collision integral is seen to be a continous operator into the same space. Furthermore, we give a new pointwise lower bound as well as asymptotic estimates for the loss term without requiring that the entropy is finite. (2000): 46E35, 47J05, 47G20, 76P05, 82C40 AMS Subject Classification

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Section: The Gain Part Of the Collision Operatormentioning

confidence: 84%

“…This investigation started in [Ar], [Gu1] and [Gu2] in the setting of weighted Lebesgue spaces for kernels with angular or Grad's cutoff condition.…”

Section: Remark 11 For the Study Of The Bilinear Operator It Is Commonmentioning

confidence: 99%

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On Estimates of the Boltzmann Collision Operator with Cut-off

Duduchava

Kirsch

Rjasanow

2005

J. math. fluid mech.

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“…Convergence to the thermodynamic equilibrium was studied in [1,9,47]. Various L p estimates and their applications were considered in [6,38,39,48]. For the propagation and creation of various types of moments estimates, see [2,3,7,8,10,11,19,26,28,49,53,45].…”

Section: Q(f G)(p)mentioning

confidence: 99%

Spatially Homogeneous Boltzmann Equation for Relativistic Particles

Strain¹,

Yun²

2014

SIAM J. Math. Anal.

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Abstract. The spatially homogeneous Boltzmann equation has been studied extensively in the Newtonian case, but not much is known for the special relativistic case. In this paper, we address several issues for the spatially homogeneous Boltzmann equation for relativistic particles. We first derive the relativistic version of the Povzner inequality. Using this, we study the Cauchy problem and investigate how the polynomial and exponential moments in L 1 are propagated. Several key differences between the relativistic and the Newtonian cases are confronted and discussed.

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“…[5,6,8,9,13] and references therein). In these works, it has been shown that the Sobolev or Lebesgue regularity satisfied by the initial datum is propagated along the time variable.…”

Section: Introductionmentioning

confidence: 99%