Related papers: On the global well-posedness for Euler equations w…

This paper investigates the well-posedness of five classes of boundary value problems for the two-dimensional steady incompressible Euler equations in an annular domain. Three of these boundary conditions can be effectively addressed using…

We establish global well-posedness for both the defocusing and focusing complex-valued modified Korteweg--de Vries equations on the real line in modulation spaces $M_p^{s,2}(\mathbb{R})$, for all $1\leq p<\infty$ and $0\leq s<3/2-1/p$. We…

In this article, we initiate the study of the Cauchy problem for the two-dimensional relativistic Euler equations in a low-regularity setting. By introducing good variables--a rescaled velocity, logarithmic enthalpy, and an appropriately…

This paper deals with the evolution of the Einstein gravitational fields which are coupled to a perfect fluid. We consider the Einstein--Euler system in asymptotically flat spacestimes and therefore use the condition that the energy density…

In this article, we study Lions' density patch problem in two space dimensions at critical regularity. We prove global existence, uniqueness, and stability for a fluid occupying a bounded Lipschitz region surrounded by vacuum and evolving…

We prove the global stability of the Minkowski space viewed as the trivial solution of the Einstein-Vlasov system. To estimate the Vlasov field, we use the vector field and modified vector field techniques developed in [FJS15; FJS17]. In…

We prove a priori estimates for the compressible Euler equations modeling the motion of a liquid with moving physical vacuum boundary in an unbounded initial domain. The liquid is under influence of gravity but without surface tension. Our…

In this paper, we investigate the persistency of loglog singular structure for 2D Euler equation under the perturbation of continuous function. First, we prove that when loglog vortex is perturbed by the function with modulus of continuity…

In this paper we consider the incompressible Euler equation in a simply-connected bounded planar domain. We study the confinement of the vorticity around a stationary point vortex. We show that the power law confinement around the center of…

In this article we consider the two-dimensional incompressible Euler equations and give a sufficient condition on Gaussian measures of jointly independent Fourier coefficients supported on $H^{\sigma}(\mathbb{T}^2)$ ($\sigma>3$) such that…

For any $2<p<\infty$ we prove that there exists an initial velocity field $v^\circ\in L^2$ with vorticity $\omega^\circ\in L^1\cap L^p$ for which there are infinitely many bounded admissible solutions $v\in C_tL^2$ to the 2D Euler equation.…

In this work we prove the weighted Gevrey regularity of solutions to the incompressible Euler equation with initial data decaying polynomially at infinity. This is motivated by the well-posedness problem of vertical boundary layer equation…

We consider uniformly rotating incompressible Euler and Navier-Stokes equations. We study the suppression of vertical gradients of Lagrangian displacement ("vertical" refers to the direction of the rotation axis). We employ a formalism that…

We consider the 3D compressible isentropic Euler equations describing the motion of a liquid in an unbounded initial domain with a moving boundary and a fixed flat bottom at finite depth. The liquid is under the influence of gravity and…

In this investigation we revisit the question of the linear stability analysis of 2D steady Euler flows characterized by the presence of compact regions with constant vorticity embedded in a potential flow. We give a complete derivation of…

This paper is about Lions' open problem on density patches \cite{LIONS}: whether inhomogeneous incompressible Navier-Stokes equations preserve the initial regularity of the free boundary given by density patches. Using classical Sobolev…

The motion of an incompressible fluid in Lagrangian coordinates involves infinitely many symmetries generated by the left Lie algebra of group of volume preserving diffeomorphisms of the three dimensional domain occupied by the fluid.…

In this paper, we investigate nonlinear stability of planar steady Euler flows related to least energy solutions of the Lane-Emden equation in a smooth bounded domain. We prove the orbital stability of these flows in terms of both the $L^s$…

Introducing a new notion of generalized suitable weak solutions, we first prove validity of the energy inequality for such a class of weak solutions to the Navier-Stokes equations in the whole space $\mathbb{R}^n$. Although we need certain…

We prove that the 2d Euler equation is globally well-posed in a space of vector fields having spatial asymptotic expansion at infinity of any a priori given order. The asymptotic coefficients of the solutions are holomorphic functions of…