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We consider the Navier-Stokes equations in a three-dimensional thin spherical shell and on the two-dimensional unit sphere, and estimate the difference of weak solutions on the thin spherical shell and the unit sphere. Assuming that the…

Analysis of PDEs · Mathematics 2025-07-10 Tatsu-Hiko Miura

In the first part of this article, we obtain a linear system whose the solution solves the time-independent incompressible Navier-Stokes system for the special case in which the external forces vector is a gradient. In a second step we…

General Mathematics · Mathematics 2019-08-27 Fabio Botelho

In this article, we consider the compressible Navier-Stokes equation with density dependent viscosity coefficients and a term of capillarity introduced by Coquel et al in \cite{5CR}. This model includes at the same time the barotropic…

Analysis of PDEs · Mathematics 2008-03-14 Boris Haspot

We prove global existence of weak solutions to two systems of equations which extend the dynamics of the Navier-Stokes equations for incompressible viscous flow with no-slip boundary condition. The systems of equations we consider arise as…

Analysis of PDEs · Mathematics 2013-08-23 Mihaela Ignatova , Gautam Iyer , James P. Kelliher , Robert L. Pego , Arghir D. Zarnescu

A model of vascular network formation is analyzed in a bounded domain, consisting of the compressible Navier-Stokes equations for the density of the endothelial cells and their velocity, coupled to a reaction-diffusion equation for the…

Analysis of PDEs · Mathematics 2023-07-10 Xiaokai Huo , Ansgar Jüngel

This paper deals with the combined incompressible quasineutral limit of the weak martingale solution of the compressible Navier-Stokes-Poisson system perturbed by a stochastic forcing term in the whole space. In the framework of…

Analysis of PDEs · Mathematics 2020-08-21 Donatella Donatelli , Prince Romeo Mensah

We consider a time-dependent coupled Navier--Stokes/generalized poroelastic flow problem and propose a unified and monolithic finite element discretization based on implicit time stepping. To handle the fluid-structure interface we employ a…

Numerical Analysis · Mathematics 2026-05-19 Aparna Bansal , Nicolas A. Barnafi , Dwijendra Narain Pandey , Ricardo Ruiz-Baier

Approximation of the marginal distribution of the solution of the stochastic Navier-Stokes equations on the two-dimensional torus by high order numerical methods is considered. The corresponding rates of convergence are obtained for a…

Numerical Analysis · Mathematics 2011-05-16 Philipp Doersek

We address the issue of existence of weak solutions for the non-homogeneous Navier-Stokes system with Navier friction boundary conditions allowing the presence of vacuum zones and assuming rough conditions on the data. We also study the…

Analysis of PDEs · Mathematics 2012-10-05 Lucas C. F. Ferreira , Gabriela Planas , Elder J. Villamizar-Roa

A general framework for the theory of statistical solutions on trajectory spaces is constructed for a wide range of equations involving incompressible viscous flows. This framework is constructed with a general Hausdorff topological space…

Analysis of PDEs · Mathematics 2015-03-24 Anne Bronzi , Cecilia Mondaini , Ricardo Rosa

Here we investigate 3-dimensional Navier-Stokes Equations in the incompressible case with use of different approach and we prove the uniqueness of the weak solutions for the data from the space, which is dense in usual space of data.…

Analysis of PDEs · Mathematics 2016-12-28 Kamal N. Soltanov

With the previous results for the analytical blowup solutions of the N-dimensional Euler-Poisson equations, we extend the similar structure to construct an analytical family of solutions for the isothermal Navier-Stokes equations and…

Mathematical Physics · Physics 2009-02-19 Manwai Yuen

A new probabilistic representation is presented for solutions of the incompressible Navier-Stokes equations in 3 dimensions with given forcing and initial velocity. This representation expresses solutions as scaled conditional expectations…

Probability · Mathematics 2007-05-23 M. Ossiander

We consider the Navier-Stokes equations in a three-dimensional curved thin domain around a given closed surface under Navier's slip boundary conditions. When the thickness of the thin domain is sufficiently small, we establish the global…

Analysis of PDEs · Mathematics 2020-12-30 Tatsu-Hiko Miura

This paper discussed the global existence of the smoothing solution for the Navier-Stokes equations. At first, we construct the theory of the linear equations which is about the unknown four variables functions with constant coefficients.…

Analysis of PDEs · Mathematics 2011-07-05 Jianfeng Wang

This paper concerns the existence of global weak solutions to the barotropic compressible Navier-Stokes equations with degenerate viscosity coefficients. We construct suitable approximate system which has smooth solutions satisfying the…

Analysis of PDEs · Mathematics 2015-11-12 Jing Li , Zhouping Xin

Starting from the partial regularity results for suitable weak solutions to the Navier-Stokes Cauchy problem by Caffarelli, Kohn and Nirenberg, as a corollary, under suitable assumptions of local character on the initial data, we prove a…

Mathematical Physics · Physics 2015-07-24 Francesca Crispo , Paolo Maremonti

We prove some estimates for suitable weak solutions to the non-stationary three-dimensional Navier-Stokes equations under assumptions that certain invariant functionals of the velocity are bounded.

Analysis of PDEs · Mathematics 2007-05-23 G Seregin

This paper is concerned with probabilistic techniques for forecasting dynamical systems described by partial differential equations (such as, for example, the Navier-Stokes equations). In particular, it is investigating and comparing…

Machine Learning · Computer Science 2025-11-07 Hans Harder , Abhijeet Vishwasrao , Luca Guastoni , Ricardo Vinuesa , Sebastian Peitz

Fluid configurations in three-dimensions, displaying a plausible decay of regularity in a finite time, are suitably built and examined. Vortex rings are the primary ingredients in this study. The full Navier-Stokes system is converted into…

Analysis of PDEs · Mathematics 2020-05-12 Daniele Funaro