Related papers: Epsilon regularity for the Navier-Stokes equations…
In this work we consider the generalized Navier-Stoke equations with the presence of a damping term in the momentum equation. % The problem studied here derives from the set of equations which govern the isothermal flow of incompressible,…
We consider the flow of two viscous and incompressible fluids within a bounded domain modeled by means of a two-phase Navier-Stokes system. The two fluids are assumed to be immiscible, meaning that they are separated by an interface. With…
We provide a rigorous derivation of the compressible Reynolds system as a singular limit of the compressible (barotropic) Navier-Stokes system on a thin domain. In particular, the existence of solutions to the Navier-Stokes system with…
For a local suitable weak solution to the Navier-Stokes equations, we prove that if the vorticity vectors belong to a double cone in regions of high vorticity magnitude, then the solution is regular. Roughly speaking this implies that, near…
In a previous paper [Jayanti, P.C., Trivisa, K. Local Existence of Solutions to a Navier-Stokes-Nonlinear-Schr\"odinger Model of Superfluidity. J. Math. Fluid Mech. 24, 46 (2022)], the authors proved the existence of local-in-time weak…
We consider the two-dimensional incompressible inhomogeneous Navier-Stokes equations with odd viscosity, where the shear and the odd viscosity coefficients depend continuously on the unknown density function. We establish the existence of…
We prove the existence of weak solutions to steady, compressible non-Newtonian Navier-Stokes system on a bounded, two- or three-dimensional domain. Assuming the viscous stress tensor is monotone satisfying a power-law growth with power $r$…
We prove the uniqueness and stability of entropy shocks to the isentropic Euler systems among all vanishing viscosity limits of solutions to associated Navier-Stokes systems. To take into account the vanishing viscosity limit, we show a…
A proof is given of the global existence and uniqueness of a weak solution to Navier-Stokes boundary problem. The proof is short and essentially self-contained.
We study conditional regularity for the compressible Navier-Stokes equations with potential temperature transport in a bounded domain $\Omega\subset\mathbb{R}^d$, $d\in\{2,3\}$, with no-slip boundary conditions. We first prove the existence…
In the note, various scenarios of potential Type II blowups of suitable weak solutions to the Navier-Stokes equations are studied. It is shown, that under some assumptions, such type of blowups cannot happen. In this case, corresponding…
We consider the Cauchy problem for the incompressible Navier-Stokes equations in $\R^3$, and provide a sufficient condition to ensure the smoothness of the solution. It involves only two entries of the velocity Hessian.
This paper extends the weak solution theory for the 3D Navier-Stokes equations of Barker, Seregin and Sverak from a critical setting to a supercritical setting making sure to include a useful a priori energy bound as well as a statement…
This paper establishes a regularity theory for the magnetohydrodynamics (MHD) equations with external forces through scaling analysis. Inspired by the existing methodology, we utilize linearized approximations and the monotonicity property…
We consider the Navier-Stokes equation in a domain with irregular boundaries. The irregularity is modeled by a spatially homogeneous random process, with typical size $\eps \ll 1$. In a parent paper, we derived a homogenized boundary…
We obtain logarithmic improvements for conditions for regularity of the Navier-Stokes equation, similar to those of Prodi-Serrin or Beale-Kato-Majda. Some of the proofs make use of a stochastic approach involving Feynman-Kac like…
In this paper, we study the weak-strong uniqueness for the Leray-Hopf type weak solutions to the Beris-Edwards model of nematic liquid crystals in $\R^3$ with an arbitrary parameter $\xi\in\R$, which measures the ratio of tumbling and…
The existence of proper weak solutions of the Dirichlet-Cauchy problem constituted by the Navier-Stokes-Fourier system which characterizes the incompressible homogeneous Newtonian fluids under thermal effects is studied. We call proper weak…
This paper gives another version of results due to Raugel and Sell, and similar results due to Moise, Temam and Ziane, that state the following: the solution of the Navier-Stokes equation on a thin 3 dimensional domain with periodic…
We consider the question of existence of weak solutions for the fully inhomogeneous, stationary generalized Navier-Stokes equations for homogeneous, shear-thinning fluids. For a shear rate exponent $p \in \big(\tfrac{2d}{d+1}, 2\big)$,…