Loading...
Please wait, while we are loading the content...
Similar Documents
On the Supercritically Diffusive Magneto-geostrophic Equ Ations
| Content Provider | Semantic Scholar |
|---|---|
| Author | Rusin, Walter Vicol, Vlad Bstract, A. |
| Copyright Year | 2012 |
| Abstract | We address the well-posedness theory for the magneto-geos trophic equation, namely an active scalar equation in which the divergence-free drift velocit y is one derivative more singular than the active scalar. In the presence of supercritical fractional diffusion give n by (−∆) with 0 < γ < 1, we discover that for γ > 1/2 the equations are locally well-posed, while for γ < 1/2 they are ill-posed, in the sense that there is no Lipschitz solution map. The main reason for the striking los s f regularity whenγ goes below1/2 is that the constitutive law used to obtain the velocity from the active scalar is given by an unbounded Fourier multiplier which is both even and anisotropic. Lastly, we note that the a nisotropy of the constitutive law for the velocity may be explored in order to obtain an improvement in the regul arity of the solutions when the initial data and the force have thin Fourier support, i.e. they are supported on a plane in frequency space. In particular, for such well-prepared data one may prove the local existence and uni que ess of solutions for all values of γ ∈ (0, 1). In fact, these solutions are global in time when γ ∈ [1/2, 1). Nonlinearity. Volume 25, Number 11 (2012), 3071–3097. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://cims.nyu.edu/~vicol/FRV1.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Contraction mapping Endometrial Stromal Sarcoma Equation:Equ:Pt:Gestational age estimation formula:Nar Nonlinear system Singular Solutions Trophic function Velocity (software development) Well-posed problem Whole Earth 'Lectronic Link |
| Content Type | Text |
| Resource Type | Article |
