Related papers: Symmetry and rigidity: Only one kind of symmetry a…
We consider the singularity formation of strong solutions to the two-dimensional full compressible Navier-Stokes equations with zero heat conduction in a bounded domain. It is shown that for the initial density allowing vacuum, the strong…
We obtain a pointwise, a priori bound for the vorticity of axis symmetric solutions to the 3 dimensional Navier-Stokes equations. The bound is in the form of a reciprocal of a power of the distance to the axis of symmetry. This seems to be…
We study the Navier-Stokes-Darcy-Boussinesq system that models the thermal convection of a fluid overlying a saturated porous medium in a general decomposed domain. In both two and three spatial dimensions, we first prove the existence of…
In a recent article, C. Bardos et. al. constructed weak solutions of the three-dimensional incompressible Euler equations which emerge from two-dimensional initial data yet become fully three-dimensional at positive times. They asked…
We demonstrate that field theories involving explicit breaking of continous symmetries, incorporate two generic classes of topological defects each of which is stable for a particular range of parameters. The first class includes defects of…
The seminal work of Coleman, Glaser, and Martin established that, at zero temperature, any non-trivial solution to the equations of motion with the least Euclidean action is $O(D)$-symmetric. This paper extends their foundational analysis…
In this paper, we prove the existence and a partial regularity of a weak solution to the system governing the interaction between a rigid body and a viscous incompressible Newtonian fluid. The evolution of the system body-fluid is studied…
This study is devoted to the incompressible and stationary Navier-Stokes equations in two-dimensional unbounded domains. First, the main results on the construction of the weak solutions and on their asymptotic behavior are reviewed and…
This paper considers the supercritical Navier-Stokes equations posed in the whole space $\R^d$, with suitably randomized initial data, in the weak solution setting. The global weak solutions are constructed for a large set of initial data…
We construct self-similar solutions to the three dimensional Navier-Stokes equations for divergence free, self-similar initial data that can be large in the critical Besov space $\dot B^{-1+3/p}_{p,\infty}$ where $3< p< 6$. We also…
Strong solutions of the non-stationary Navier-Stokes equations under non-linearized slip or leak boundary conditions are investigated. We show that the problems are formulated by a variational inequality of parabolic type, to which…
This paper is concerned with geometric regularity criteria for the Navier-Stokes equations in $\mathbb{R}^3_{+}\times (0,T)$ with no-slip boundary condition, with the assumption that the solution satisfies the `ODE blow-up rate' Type I…
We study the three-dimensional Navier-Stokes equations in the presence of the axisymmetric linear strain, where the strain rate depends on time in a specific manner. It is known that the system admits solutions which blow up in finite time…
Recently, strong evidence has accumulated that some solutions to the Navier-Stokes equations in physically meaningful classes are not unique. The primary purpose of this paper is to establish necessary properties for the error of…
We consider the three-dimensional steady Navier-Stokes system in the exterior of an infinite cylinder under the action of an external force. We construct solutions in the class of vertically uniform flows which vanish at horizontal…
In this paper, we consider nonsymmetric solutions to certain Lyapunov and Riccati equations and inequalities with coefficient matrices corresponding to cone-preserving dynamical systems. Most results presented here appear to be novel even…
In this article, we use the decay character of initial data to compare the energy decay rates of solutions to different compressible approximations to the Navier-Stokes equations. We show that the system having a nonlinear damping term has…
In this paper we consider a coupled hydrodynamical system which involves the Navier-Stokes equations for the velocity field and kinematic transport equations for the molecular orientation field. By applying the Chemin-Lerner's time-space…
We propose a local notion of strong-to-weak spontaneous symmetry breaking (SW-SSB), through a local one-point fidelity correlator. Compared with the previous definition in terms of a two-point fidelity correlator, our local formulation…
Spontaneous symmetry breaking is a general principle, that constitutes the underlying concept of a vast number of physical phenomena ranging from ferromagnetism and superconductivity in condensed matter physics to the Higgs mechanism in the…