Low regularity of non-L^2(R^n) local solutions to gMHD-alpha systems
| dc.contributor.author | Riva, Lorenza | |
| dc.contributor.author | Pennington, Nathan | |
| dc.date.accessioned | 2021-09-29T18:49:51Z | |
| dc.date.available | 2021-09-29T18:49:51Z | |
| dc.date.issued | 2020-05-28 | |
| dc.description.abstract | The Magneto-Hydrodynamic (MHD) system of equations governs viscous fluids subject to a magnetic field and is derived via a coupling of the Navier-Stokes equations and Maxwell's equations. Recently is has become common to study generalizations of fluids-based differential equations. Here we consider the generalized Magneto-Hydrodynamic alpha (gMHD-α) system, which differs from the original MHD system by including an additional non-linear terms (indexed by α), and replacing the Laplace operators by more general Fourier multipliers with symbols of the form -|ξ|γ/g(|ξ|). In [8], the problem was considered with initial data in the Sobolev space Hs,2(ℝn) with n ≥ 3. Here we consider the problem with initial data in Hs,p(ℝn) with n ≥ 3 and p > 2. Our goal is to minimizing the regularity required for obtaining uniqueness of a solution. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 17 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Riva, L., & Pennington, N. (2020). Low regularity of non-L^2(R^n) local solutions to gMHD-alpha systems. <i>Electronic Journal of Differential Equations, 2020</i>(54), pp. 1-17. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14561 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2020, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Generalized MHD-alpha | |
| dc.subject | Local solution | |
| dc.subject | Low regularity | |
| dc.title | Low regularity of non-L^2(R^n) local solutions to gMHD-alpha systems | |
| dc.type | Article |