ترغب بنشر مسار تعليمي؟ اضغط هنا

Projective properties of Divergence-free symmetric tensors, and new dispersive estimates in gas dynamics

82   0   0.0 ( 0 )
 نشر من قبل Denis Serre
 تاريخ النشر 2021
  مجال البحث فيزياء
والبحث باللغة English
 تأليف Denis Serre




اسأل ChatGPT حول البحث

The class of Divergence-free symmetric tensors is ubiquitous in Continuum Mechanics. We show its invariance under projective transformations of the independent variables. This action, which preserves the positiveness, extends Sophus Lies group analysis of Newtonian dynamics.When applied to models of gas dynamics --~such as Euler system or Boltzmann equation,~-- in combination with Compensated Integrability, this yields new dispersive estimates. The most accurate one is obtained for mono-atomic gases. Then the space-time integral of $trho^frac1d p$ is bounded in terms of the total mass and moment of inertia alone.



قيم البحث

اقرأ أيضاً

91 - Denis Serre 2021
Divergence-free symmetric tensors seem ubiquitous in Mathematical Physics. We show that this structure occurs in models that are described by the so-called second variational principle, where the argument of the Lagrangian is a closed differential fo rm. Divergence-free tensors are nothing but the second form of the Euler--Lagrange equations. The symmetry is associated with the invariance of the Lagrangian density upon the action of some orthogonal group.
We present sharp conditions on divergence-free drifts in Lebesgue spaces for the passive scalar advection-diffusion equation [ partial_t theta - Delta theta + b cdot abla theta = 0 ] to satisfy local boundedness, a single-scale Harnack inequality, and upper bounds on fundamental solutions. We demonstrate these properties for drifts $b$ belonging to $L^q_t L^p_x$, where $frac{2}{q} + frac{n}{p} < 2$, or $L^p_x L^q_t$, where $frac{3}{q} + frac{n-1}{p} < 2$. For steady drifts, the condition reduces to $b in L^{frac{n-1}{2}+}$. The space $L^1_t L^infty_x$ of drifts with `bounded total speed is a borderline case and plays a special role in the theory. To demonstrate sharpness, we construct counterexamples whose goal is to transport anomalous singularities into the domain `before they can be dissipated.
224 - Jeremy Marzuola 2009
We develop the techniques of cite{KS1} and cite{ES1} in order to derive dispersive estimates for a matrix Hamiltonian equation defined by linearizing about a minimal mass soliton solution of a saturated, focussing nonlinear Schrodinger equation {c} i u_t + Delta u + beta (|u|^2) u = 0 u(0,x) = u_0 (x), in $reals^3$. These results have been seen before, though we present a new approach using scattering theory techniques. In further works, we will numerically and analytically study the existence of a minimal mass soliton, as well as the spectral assumptions made in the analysis presented here.
We investigate the dispersive properties of solutions to the Schrodinger equation with a weakly decaying radial potential on cones. If the potential has sufficient polynomial decay at infinity, then we show that the Schrodinger flow on each eigenspac e of the link manifold satisfies a weighted $L^1to L^infty$ dispersive estimate. In odd dimensions, the decay rate we compute is consistent with that of the Schrodinger equation in a Euclidean space of the same dimension, but the spatial weights reflect the more complicated regularity issues in frequency that we face in the form of the spectral measure. In even dimensions, we prove a similar estimate, but with a loss of $t^{1/2}$ compared to the sharp Euclidean estimate.
124 - Denis Serre 2019
We consider the motion of a finite though large number of particles in the whole space R n. Particles move freely until they experience pairwise collisions. We use our recent theory of divergence-controlled positive symmetric tensors in order to esta blish two estimates regarding the set of collisions. The only information needed from the initial data is the total mass and the total energy.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا