View Proposal #533
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| ID | 533 |
|---|---|
| First Name | Lorenzo |
| Last Name | Riva |
| Institution | Creighton University |
| Speaker Category | undergraduate student |
| Title of Talk | Low Regularity Non-$L^2(\mathbb{R}^n)$ Local Solutions to the gMHD-$\alpha$ system |
| 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. It has recently become common to study generalizations of fluids-based differential equations. Here we consider the generalized Magneto-Hydrodynamic alpha (gMHD-$\alpha$) system, which differs from the original MHD system by the presence of additional non-linear terms (indexed by the choice of $\alpha$) and replacing the Laplace operators in the equations by more general Fourier multipliers with symbols of the form $-\vert \xi \vert^\gamma / g(\vert \xi \vert)$. In \cite{penn1}, the author considered the problem with initial data in Sobolev spaces of the form $H^{s,2}(\mathbb{R}^n)$ with $n \geq 3$. Here we consider the problem with initial data in $H^{s,p}(\mathbb{R}^n)$ with $n \geq 3$ and $p > 2$, with the goal of minimizing the regularity required to obtain unique existence results. |
| Subject area(s) | Analysis, PDEs |
| Suitable for undergraduates? | N |
| Day Preference | Either |
| Computer Needed? | N |
| Bringing a laptop? | Y |
| Overhead Needed? | Y |
| Software requests | |
| Special Needs | |
| Date Submitted | 09/16/2019 |
| Year | 2019 |