相关论文: On the locally self-similar singular solutions for…

In this article we consider the discretely self-similar singular solutions of the Euler equations, and the possible velocity profiles concerned not only have decaying spatial asymptotics, but also have unconventional non-decaying…

We investigate the axisymmetric incompressible Euler equations without swirl in $\mathbb R^d$ with $d\geq 3$. For any $\alpha\in(0, \alpha_d)$, where $\alpha_d=1-2/d$, we construct a self-similar blow-up solution whose initial velocity…

We consider a sequence of approximate solutions to the compressible Euler system admitting uniform energy bounds and/or satisfying the relevant field equations modulo an error vanishing in the asymptotic limit. We show that such a sequence…

We investigate multidimensional model for incompressible non-Newtonian fluids. Using method of energy estimates we prove the property of finite speed of propagations of the solution support for this problem. We find sharp bounds of the…

This paper addresses the construction and the stability of self-similar solutions to the isentropic compressible Euler equations. These solutions model a gas that implodes isotropically, ending in a singularity formation in finite time. The…

In this paper we rule out the possibility of asymptotically self-similar singularities for both of the 3D Euler and the 3D Navier-Stokes equations. The notion means that the local in time classical solutions of the equations develop…

For the incompressible and the isentropic compressible Euler equations in arbitrary space dimension, we establish the principle of localised relative energy, thus generalising the well-known relative energy method. To this end, we adapt…

In this brief note we show that the author's previous result in \cite{cha} on the nonexistence of self-similar singularities for the 3D incompressible Euler equations implies actually the nonexistence of `locally self-similar' singular…

We consider 3D micropolar flows with possible vanishing spin viscosity and investigate the decay of the energy for large times. We compute first the exact $L^2$-asymptotic profile, as $t\to+\infty$, for solutions to the linear 3D micropolar…

We show that weak solutions of degenerate Navier-Stokes equations converge to the strong solutions of the pressureless Euler system with linear drag term, Newtonian repulsion and quadratic confinement. The proof is based on the relative…

We consider several modifications of the Euler system of fluid dynamics including its pressureless variant driven by non-local interaction repulsive-attractive and alignment forces in the space dimension $N=2,3$. These models arise in the…

We introduce a natural notion of incompressibility for fluids governed by the relativistic Euler equations on a fixed background spacetime, and show that the resulting equations reduce to the incompressible Euler equations in the classical…

We study the solutions of the nonstationary incompressible Navier--Stokes equations in $\R^d$, $d\ge2$, of self-similar form $u(x,t)=\frac{1}{\sqrt t}U\bigl(\frac{x}{\sqrt t}\bigr)$, obtained from small and homogeneous initial data $a(x)$.…

In this paper, we showed that for some given suitable density and pressure, there exist infinitely many compactly supported solutions with prescribed energy profile. The proof is mainly based on the convex integration scheme. We construct…

We establish an asymptotic profile that sharply describes the behavior as $t\to\infty$ for solutions to a non-solenoidal approximation of the incompressible Navier-Stokes equations introduced by Temam. The solutions of Temam's model are…

We study scenarios of self-similar type blow-up for the incompressible Navier-Stokes and the Euler equations. The previous notions of the discretely (backward) self-similar solution and the asymptotically self-similar solution are…

We present a local existence result for the three dimensional incompressible Euler equations. The solution is constructed using a formulation of the equations as an active vector system in Eulerian coordinates. The formulation employs the…

We introduce a new model of the nonlocal wave equations with a logarithmic damping mechanism. We consider the Cauchy poroblem for the new model in the whole space. We study the asymptotic profile and optimal decay and blowup rates of…

The paper addresses the question of existence of a locally self-similar blow-up for the incompressible Euler equations. Several exclusion results are proved based on the $L^p$-condition for velocity or vorticity and for a range of scaling…

We are concerned on the study of the unique continuation type property for the 3D incompressible Euler equations in the self-similar type form. Discretely self-similar solution is a generalized notion of the self-similar solution, which is…