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In this research, the Cauchy problem of the 3D viscous Boussinesq system is studied considering an initial temperature with negative Sobolev regularity. Precisely, we construct local in time mild solutions to this system where the temperature term be
Externí odkaz:
http://arxiv.org/abs/2404.13243
This paper investigates new fractional energy methods for variables coupling the Navier-Stokes equations. Micropolar fluids starting from an initial angular velocity with Sobolev regularity close to $-1/2$ are constructed.
Comment: 10 pages
Comment: 10 pages
Externí odkaz:
http://arxiv.org/abs/2401.16554
In this paper we develop new methods to obtain regularity criteria for the three-dimensional Navier-Stokes equations in terms of dynamically restricted endpoint critical norms: the critical Lebesgue norm in general or the critical weak Lebesgue norm
Externí odkaz:
http://arxiv.org/abs/2302.06509
We consider a family of weights which permit to generalize the Leray procedure to obtain weak suitable solutions of the 3D incom-pressible Navier-Stokes equations with initial data in weighted L 2 spaces. Our principal result concerns the existence o
Externí odkaz:
http://arxiv.org/abs/2010.00868
Publikováno v:
Acta Applicandae Mathematicae 176 (2021), No. 1, Article No. 10, 10 pp
We give some conditions under which the pressure term in the incompressible Navier-Stokes equations on the entire $d$-dimensional Euclidean space is determined by the formula $\displaystyle \nabla p = \nabla \left(\sum_{i,j=1}^d \mathcal{R}_i \mathca
Externí odkaz:
http://arxiv.org/abs/2004.02588
We consider here the magneto-hydrodynamics (MHD) equations on the whole space. For the 3D case, in the setting of the weighted $L^2$ spaces we obtain a weak-strong uniqueness criterion provided that the velocity field and the magnetic field belong to
Externí odkaz:
http://arxiv.org/abs/2002.10531
We characterise the pressure term in the incompressible 2D and 3D Navier-Stokes equations for solutions defined on the whole space.
Externí odkaz:
http://arxiv.org/abs/2001.10436
Akademický článek
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This paper deals with the existence of global weak solutions for 3D MHD equations when the initial data belong to the weighted spaces $L^2_{w_\gamma}$, with $w_\gamma(x)=(1+| x|)^{-\gamma}$ and $0 \leq \gamma \leq 2$. Moreover, we prove the existence
Externí odkaz:
http://arxiv.org/abs/1910.11267
We show the existence of global weak solutions of the 3D Navier-Stokes equations with initial velocity in the weighted spaces L 2 w$\gamma$ , where w $\gamma$ (x) = (1 + |x|) --$\gamma$ and 0 < $\gamma$ $\le$ 2, using new energy controls. As applicat
Externí odkaz:
http://arxiv.org/abs/1906.11038