View Proposal #533
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ID | 533 |
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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 |