Fujita Kato solution for compressible Navier-Stokes equation with axisymmetric initial data and zero Mach number limit
Haspot, Boris (2019), Fujita Kato solution for compressible Navier-Stokes equation with axisymmetric initial data and zero Mach number limit, Communications in Contemporary Mathematics. 10.1142/S021919971950041X
TypeArticle accepté pour publication ou publié
Journal nameCommunications in Contemporary Mathematics
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CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)In this paper we investigate the question of the existence of global strong solution for the compressible Navier Stokes equations for small initial data such that the rotational part of the velocity Pu 0 belongs to ˙ H N 2 −1. We show then an equivalence of the so called Fujita Kato theorem to the case of the compressible Navier-Stokes equation when we consider axisymmetric initial data in dimension N = 2, 3. The main difficulty is relied to the fact that in this case the velocity is not Lipschitz, in consequence we have to study carefully the coupling between the rotational and irrotational part of the velocity. In a second part, following the arguments developed in  we adress the question of convergence to the incompressible model (for ill-prepared initial data) when the Mach number goes to zero.
Subjects / KeywordsCompressible Navier–Stokes equation; saxisymmetric initial data; existence of global strong solution; Mach number limit; ill prepared initial data
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