论文标题
vlasov-riesz系统的适应性和奇异性形成
Well-posedness and singularity formation for Vlasov--Riesz system
论文作者
论文摘要
我们研究了Vlasov-Riesz系统的Cauchy问题，该系统是一个vlasov方程式，具有相互作用的潜在推广先前研究的案例，包括库仑$φ=（-Δ）^{ - 1}ρ$，manev $（ - δ） $（ - δ）^{ - \ frac12} $势。我们第一次将经典解决方案的当地理论扩展到比Manev更为单数的潜力。然后，我们为具有各种有吸引力的相互作用电位的解决方案获得有限的时间奇异性形成，从而扩展了Horst以$ d \ ge4 $的吸引人的弗拉索夫（Vlasov）的众所周知的爆炸结果。我们的局部适合性和奇异性的形成结果扩展到存在速度的线性扩散和阻尼时。
We investigate the Cauchy problem for the Vlasov--Riesz system, which is a Vlasov equation featuring an interaction potential generalizing previously studied cases, including the Coulomb $Φ= (-Δ)^{-1}ρ$, Manev $(-Δ)^{-1} + (-Δ)^{-\frac12}$, and pure Manev $(-Δ)^{-\frac12}$ potentials. For the first time, we extend the local theory of classical solutions to potentials more singular than that for the Manev. Then, we obtain finite-time singularity formation for solutions with various attractive interaction potentials, extending the well-known blow-up result of Horst for attractive Vlasov--Poisson for $d\ge4$. Our local well-posedness and singularity formation results extend to cases when linear diffusion and damping in velocity are present.
