rotation. these solutions are axisymmetric, of sobolev regularity, have non-vanishing swirl and scatter linearly, thanks to the dispersive effect induced by the rotation. to establish this, we introduce a frame
In (Comm Pure Appl Math 62(4):502–564, 2009 ), Hou and Lei proposed a 3D model for the axisymmetric incompressible Euler and Navier–Stokes equations with swirl. This model shares a number of properties of the 3D incompressible Euler and Navier–Stokes equations. In this paper, we prove...
In the present paper, we consider the two-dimensional Euler-Boussinesq equations with temperature-dependent thermaldiffusivity. More precisely, we prove the global-in-time existence and uniqueness for this system under Yudovich-type initial data. In addition, the global propagation of striated regularit...
GLOBAL EXISTENCE FOR THE AXISYMMETRIC EULER EQUATIONS 3 ii) The space B 0 ∞,1 is defined by the set of v ∈ S ′ (R 3 ) such that v e B 0 ∞,1 := q≥−1 v −S q v L ∞ < ∞. See also next section for the definition of the operator S q . iii) For ...
We consider the three-dimensional incompressible Euler equation inR3,{∂tU+U⋅∇U+∇P=0∇⋅U=0U(x,0)=U0(x). The equation describes the motion of an ideal incompressible fluid inR3with initial velocityU0(x). HereU=(U1,U2,U3):R3×R→R3represents the velocity andP:R3×R→R...
Some features of this article are the following: (i) we do not require the initial data to be axisymmetric; (ii) the Sobolev exponent s can be an arbitrary big positive integer; and (iii) the explicit asymptotic expansion formulas of Sobolev regular solution is given. The key point of ...
We work in two space dimensions and start with initial data which are rotation invariant around 0 and of the type considered by Serre and Grassin–Serre. We then consider slightly perturbed initial data which are also rotation invariant around 0 and jump across a given circle centered at 0, ...
With the additional swirl-free assumption, our first main result gives local wellposedness of Yudovich-type solutions, extending the work of Danchin (2007) [9] for axisymmetric flows in R 3 . The second main result establishes global wellposedness under additional decay conditions near the axes...
Global centered waves and contact discontinuities for the axisymmetric Euler equations of certain isentropic perfect gases in two space dimensionsisentropic Euler equationsglobal solutionscentered wavescontact discontinuitiesSMOOTH SOLUTIONSCOMPRESSIBLE FLUIDSPERFECT GAS...
For 2D compressible full Euler equations of Chaplygin gases, when the initial axisymmetric perturbation of a rest state is small, we prove that the smooth solution exists globally. Compared with the previous references, there are two different key points in this paper: both the vorticit...