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The fully compressible semi-geostrophic system is widely used in the modelling of large-scale atmospheric flows. In this paper, we prove rigorously the existence of weak Lagrangian solutions of this system, formulated in the original physical coordinates. In addition, we provide an alternative proof of the earlier result on the existence of weak solutions of this system expressed in the so-called geostrophic, or dual, coordinates. The proofs are based on the optimal transport formulation of the problem and on recent general results concerning transport problems posed in the Wasserstein space of probability measures.
We carry out extended symmetry analysis of the (1+2)-dimensional Boiti-Leon-Pempinelli system, which enhances and generalizes many results existing in the literature. The complete point-symmetry group of this system is computed using an original mega
begin{abstract} We show that if the initial profile $qleft( xright) $ for the Korteweg-de Vries (KdV) equation is essentially semibounded from below and $int^{infty }x^{5/2}leftvert qleft( xright) rightvert dx<infty,$ (no decay at $-infty$ is require
The compressible Navier-Stokes-Poisson system is concerned in the present paper, and the global existence and uniqueness of the strong solution is shown in the framework of hybrid Besov spaces in three and higher dimensions.
In arXiv:1201.4067 and arXiv:1611.08030, Eyink and Shi and Chibbaro et al., respectively, formally derived an infinite, coupled hierarchy of equations for the spectral correlation functions of a system of weakly interacting nonlinear dispersive waves
In this paper we continue the formal analysis of the long-time asymptotics of the homoenergetic solutions for the Boltzmann equation that we began in [18]. They have the form $fleft( x,v,tright) =gleft(v-Lleft( tright) x,tright) $ where $Lleft( trigh