相关论文: A remark on global solutions to random 3D vorticit…
In this paper, we establish global strong solutions for arbitrarily large initial data to the 2D and 3D compressible Navier-Stokes-Korteweg system, also referred to as the quantum Navier-Stokes equations, originally derived by Dunn and…
This article is concerned with the almost sure existence of global solutions for initial value problems of the form $\dot{\gamma}(t)= v(t,\gamma(t))$ on separable dual Banach spaces. We prove a general result stating that whenever there…
The existence and uniqueness of the global strong solution with small initial data to the three-dimensional viscoelastic fluids is established.
We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with $(-1)$-homogeneous initial data has a global scale-invariant solution which is smooth for positive times. Our main technical tools are…
Solutions to the compressible Euler equations in all dimensions have been shown to develop finite-time singularities from smooth initial data such as shocks and cusps. There is an extraordinary list of results on this subject. When the…
This article considers the spatially inhomogeneous, non-cutoff Boltzmann equation. We construct a large-data classical solution given bounded, measurable initial data with uniform polynomial decay of mild order in the velocity variable. Our…
We show existence of global strong solutions with large initial data on the irrotational part for the shallow-water system in dimension $N\geq 2$. We introduce a new notion of \textit{quasi-solutions} when the initial velocity is assumed to…
We consider the problem of global in time existence and uniqueness of solutions of the 3-D infinite depth full water wave problem. We show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher…
We present two different approaches to stochastic integration in frictionless model free financial mathematics. The first one is in the spirit of It\^o's integral and based on a certain topology which is induced by the outer measure…
Motivated by the probabilistic representation for solutions of the Navier-Stokes equations, we introduce a novel class of stochastic differential equations that depend on the entire flow of its time marginals. We establish the existence and…
Motivated by the recent advances in the theory of stochastic partial differential equations involving nonlinear functions of distributions, like the Kardar-Parisi-Zhang (KPZ) equation, we reconsider the unique solvability of one-dimensional…
We consider the 2D Euler equation with bounded initial vorticity and perturbed by rough transport noise. We show that there exists a unique solution, which coincides with the starting condition advected by the Lagrangian flow. Moreover, the…
In this paper we will prove that the vorticity belongs to L1(0; T ; L2(R3)) for the Cauchy problem of 3D incompressible Navier-Stokes equation, then the existence of a global smooth solution is obtained. Our approach is to construct a set…
We construct H\"older continuous, global-in-time probabilistically strong solutions to 3D Euler equations perturbed by Stratonovich transport noise. Kinetic energy of the solutions can be prescribed a priori up to a stopping time, that can…
We study the global existence and uniqueness of classical solutions to the three-dimensional compressible isentropic Navier-Stokes equations with vacuum and external potential forces which could be arbitrarily large provided the initial…
We show the existence of global solution for the Wadati-Konno-Ichikawa (WKI) equation with small initial data in the smooth function space. Our approach is based on the scattering and inverse scattering maps in the weighted Sobolev spaces…
We address the global existence of solutions to the stochastic Navier-Stokes equations with multiplicative noise and with initial data in $H^{1/2}(\mathbb{T}^{3})$. We prove that the solution exists globally in time with probability…
The theory of one-dimensional stochastic differential equations driven by Brownian motion is classical and has been largely understood for several decades. For stochastic differential equations with jumps the picture is still incomplete,…
This paper deals with the existence of global weak solutions for 3D MHD equations when the initial data belong to the weighted spaces $L^2_{w_\gamma}$, with $w_\gamma(x)=(1+| x|)^{-\gamma}$ and $0 \leq \gamma \leq 2$. Moreover, we prove the…
In this paper, we are concerned with the global wellposedness of 2-D density-dependent incompressible Navier-Stokes equations with variable viscosity, in a critical functional frame- work which is invariant by the scaling of the equations…