Weak Solutions of 2-D Euler Equations with Initial Vorticity in L(Log L)
نویسندگان
چکیده
منابع مشابه
Existence of Axisymmetric Weak Solutions of the 3-d Euler Equations for Near-vortex-sheet Initial Data
We study the initial value problem for the 3-D Euler equation when the fluid is inviscid and incompressible, and flows with axisymmetry and without swirl. On the initial vorticity ω0, we assumed that ω0/r belongs to L(logL(R3))α with α > 1/2, where r is the distance to an axis of symmetry. To prove the existence of weak global solutions, we prove first a new a priori estimate for the solution. ...
متن کاملOn the Axisymmetric Euler Equations with Initial Vorticity in Borderline Spaces of Besov Type
Borderline spaces of Besov type consist of tempered distributions satisfying the property that the partial sums of their B ∞,1-norm diverge in a controlled way. We prove an existence and uniqueness result for the three-dimensional axisymmetric Euler equations without swirl when initial vorticity belongs to these spaces. We also prove that for this class of solutions the vanishing viscosity limi...
متن کاملConvergence of Vortex Methods for Weak Solutions to the 2-D Euler Equations with Vortex Sheet Data
We prove the convergence of vortex blob methods to classical weak solutions for the twodimensional incompressible Euler equations with initial data satisfying the conditions that the vorticity is a finite Radon measure of distinguished sign and the kinetic energy is locally bounded. This includes the important example of vortex sheets. The result is valid as long as the computational grid size ...
متن کاملWeak Vorticity Formulation for the Incompressible 2d Euler Equations in Domains with Boundary
In this article we examine the interaction of incompressible 2D flows with compact material boundaries. Our focus is the dynamic behavior of the circulation of velocity around boundary components and the possible exchange between flow vorticity and boundary circulation in flows with vortex sheet initial data. We formulate our results for flows outside a finite number of smooth obstacles. Our po...
متن کاملGlobal Existence and Uniqueness of Weak Solutions of 3-d Euler Equations with Helical Symmetry in the Absence of Vorticity Stretching
We prove uniqueness and existence of the weak solutions of Euler equations with helical symmetry, with initial vorticity in L∞ under ”no vorticity stretching” geometric constraint. Our article follows the argument of the seminal work of Yudovich. We adjust the argument to resolve the difficulties which are specific to the helical symmetry.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1993
ISSN: 0022-0396
DOI: 10.1006/jdeq.1993.1052