We study the spectral stability of a family of periodic standing wave solutions to the generalized KdV (g-KdV) in a neighborhood of the origin in the spectral plane using what amounts to a rigorous Whitham modulation theory calculation. In particular we are interested in understanding the role played by the null directions of the linearized operator in the stability of the traveling wave to per...

In this paper, we investigate a compactness property of the linearized Boltzmann operator in context polyatomic gas whose molecules undergo resonant collisions. The peculiar structure collision rules allows to tensorize problem into velocity-related one, neighbouring monatomic case, and an internal energy-related one. Our analysis is based on specific treatment energy contributions. We also pro...

The linearized collision operator of the Boltzmann equation can in a natural way be written as sum positive multiplication operator, frequency, and an integral operator. Compactness for monatomic single species is classical result, while corresponding results mixtures polyatomic where polyatomicity modeled by discrete internal energy variable, are more recently obtained. In this work compactnes...

In this article we study the Gevrey regularization effect for spatially inhomogeneous Boltzmann equation without angular cutoff. This is partially elliptic in velocity direction and degenerates spatial variable. We consider nonlinear Cauchy problem fluctuation around Maxwellian distribution prove that any solution with mild regularity will become smooth class at positive time index depending on...

A new approach, referred to as the accelerated iterative method (AIM), is developed for obtaining steady atmospheric responses with a zonally varying basic state. The linear dynamical operator is divided into two parts, one associated with the zonally symmetric component and the other with the asymmetric component of the basic state. To ensure an accelerated convergence of the iteration to the ...