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GelfandShilov smoothing properties of the radially symmetric spatially homogeneous Boltzmann equation without angular cutoff, preprint
, 2012
"... Abstract. We prove that the Cauchy problem associated to the radially symmetric spatially homogeneous noncutoff Boltzmann equation with Maxwellian molecules enjoys the same GelfandShilov regularizing effect as the Cauchy problem defined by the evolution equation associated to a fractional harmonic ..."
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Abstract. We prove that the Cauchy problem associated to the radially symmetric spatially homogeneous noncutoff Boltzmann equation with Maxwellian molecules enjoys the same GelfandShilov regularizing effect as the Cauchy problem defined by the evolution equation associated to a fractional harmonic oscillator. 1.
A REMARK ON THE ULTRAANALYTIC SMOOTHING PROPERTIES OF THE SPATIALLY HOMOGENEOUS LANDAU EQUATION
"... Abstract. We consider the nonlinear spatially homogeneous Landau equation with Maxwellian molecules in a closetoequilibrium framework and show that the Cauchy problem for the fluctuation around the Maxwellian equilibrium distribution enjoys a GelfandShilov regularizing effect in the class S 1/2 ..."
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Abstract. We consider the nonlinear spatially homogeneous Landau equation with Maxwellian molecules in a closetoequilibrium framework and show that the Cauchy problem for the fluctuation around the Maxwellian equilibrium distribution enjoys a GelfandShilov regularizing effect in the class S 1/2 1/2 (Rd), implying the ultraanalyticity of both the fluctuation and its Fourier transform, for any positive time. 1.