عنوان

Affine Solutions of Two Dimensional Magnetohydrodynamics and Related Quadratically Coupled Transport Equations

شماره

TL0696v7wp

زبان متن نوشتاري يا گفتاري و مانند آن

انگلیسی

عنوان اصلي

Affine Solutions of Two Dimensional Magnetohydrodynamics and Related Quadratically Coupled Transport Equations

نام عام مواد

[Thesis]

نام نخستين پديدآور

Roberts, Jay

نام ساير پديدآوران

Sideris, Thomas C

نام ناشر، پخش کننده و غيره

UC Santa Barbara

تاریخ نشرو بخش و غیره

2019

کسي که مدرک را اعطا کرده

UC Santa Barbara

امتياز متن

2019

متن يادداشت

This is a dissertation on the motion of incompressible charged and non charged particles in a fluid. Specifically, we are concerned with the affine motion of such two dimensional fluids. The physical quanitities of the fluid are derived in terms of the deformation gradient which reduces the Incompressible Euler Equations (EE) and the Incompressible Ideal Magnetohydrodynamical (MHD) equations to ordinary differential equations on SL(2,\mathbb{R}). The EE and MHD become the equations of a free particle and harmonic oscillator, respectively, constrained to SL(2,\mathbb{R}) with the magnetic field strength acting as a bifurcation parameter between the two types of dynamics. We analyze the geometry of SL(2,\mathbb{R}) and completely characterize the behavior of all affine solutions. Inspired by the decay of the pressure for affine solutions to EE we analyze a related system of quadratically coupled transport equations. By smoothing the equation we show local well posedness in a generalized Sobolev space along with coupled energy estimates for a low and high energy. These estimates are inherited by the non-smoothed solution which, along with weighted energy estimates, allow us to show global well posedness for small data.

مستند نام اشخاص تاييد نشده

Roberts, Jay

مستند نام اشخاص تاييد نشده

Sideris, Thomas C

مستند نام تنالگان تاييد نشده

UC Santa Barbara

نام الکترونيکي

فرمت انتشار

p

نوع ماده

[Thesis]

کد کاربرگه

276903

سطح دسترسي

a

تكميل شده

Y