127 citations · 270 across the 7 of their papers we have counts for
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Smoothing effect of weak solutions for the spatially homogeneous Boltzmann Equation without angular cutoff
Radjesvarane Alexandre, Yoshinori Morimoto, Seiji Ukai +2
In this paper, we consider the spatially homogeneous Boltzmann equation without angular cutoff. We prove that every weak solution to the Cauchy problem with finite moments of…
Bounded Solutions of the Boltzmann Equation in the Whole Space
Radjesvarane Alexandre, Yoshinori Morimoto, Seiji Ukai +2
We construct bounded classical solutions of the Boltzmann equation in the whole space without specifying any limit behaviors at the spatial infinity and without assuming the smalln…
The Boltzmann equation without angular cutoff in the whole space: III, Qualitative properties of solutions
Radjesvarane Alexandre, Yoshinori Morimoto, Seiji Ukai +2
This is a continuation of our series of works for the inhomogeneous Boltzmann equation. We study qualitative properties of classical solutions, precisely, the full regularization i…
Boltzmann equation without angular cutoff in the whole space: I, Global existence for soft potential
Radjesvarane Alexandre, Yoshinori Morimoto, Seiji Ukai +2
It is known that the singularity in the non-cutoff cross-section of the Boltzmann equation leads to the gain of regularity and gain of weight in the velocity variable. By defining…
The Boltzmann equation without angular cutoff in the whole space: II, Global existence for hard potential
Radjesvarane Alexandre, Y. Morimoto, Seiji Ukai +2
As a continuation of our series works on the Boltzmann equation without angular cutoff assumption, in this part, the global existence of solution to the Cauchy problem in the whole…
Global existence and full regularity of the Boltzmann equation without angular cutoff
Radjesvarane Alexandre, Y. Morimoto, Seiji Ukai +2
We prove the global existence and uniqueness of classical solutions around an equilibrium to the Boltzmann equation without angular cutoff in some Sobolev spaces. In addition, the…
Regularizing effect and local existence for non-cutoff Boltzmann equation
Radjesvarane Alexandre, Y. Morimoto, Seiji Ukai +2
The Boltzmann equation without Grad's angular cutoff assumption is believed to have regularizing effect on the solution because of the non-integrable angular singularity of the cro…
A symmetrization of the relativistic Euler equations in several spatial variables
Philippe G. LeFloch, Seiji Ukai
We consider the Euler equations governing relativistic compressible fluids evolving in the Minkowski spacetime with several spatial variables. We propose a new symmetrization which…