1. 证明了高维可压缩Navier-Stokes方程组平面疏散波的大时间稳定性,是高维具有物理粘性的守恒律方程组平面基本波的渐近稳定性的第一个结果。
2. 建立了双极Vlasov-Poisson-Boltzmann方程组新的微观-宏观分解,并利用此分解证明了双极Vlasov-Poisson-Boltzmann组粘性激波、疏散波及其与接触间断波组成的复合波的稳定性。首次发现并推导出了双极VPB方程组中电场强度满足一个带阻尼的非线性扩散型方程,利用这个新的扩散型方程,克服了电场项带来的主要困难,证明了具有双极电场效应的VPB方程组基本波的渐近稳定性。德国数学文摘(ZbMATH)评论员Dimitar A. Kolev教授评论到:“本文证明了两类典型的非线性波(粘性激波和疏散波)的时间渐近稳定性(The time-asymptotic stability of the two typical nonlinear wave patterns, viscous shock waves and rarefaction waves)”。
发表论文
1. Lin-an Li, Teng Wang, Yi Wang, Stability of planar rarefaction wave to 3D full compressible Navier-Stokes equations. Arch. Rational Mech. Anal., 230 (2018), 911-937.
2. Lin-an Li, Yi Wang, Stability of the planar rarefaction wave to the two-dimensional compressible Navier-Stokes equations. SIAM J. Math. Anal., 50 (2018), 4937-4963.
3. Hailiang Li, Yi Wang, Tong Yang, Ming Ying Zhong, Stability of nonlinear wave patterns to the bipolar Vlasov-Poisson-Boltzmann system. Arch. Ration. Mech. Anal., 228 (2018), 39-127.
4. Hailiang Li, Teng Wang, Yi Wang, Stability of the superposition of a viscous contact wave with two rarefaction waves to the bipolar Vlasov-Poisson-Boltzmann system. SIAM J. Math. Anal., 50 (2018), 1829-1876.
5. Quansen Jiu, Yi Wang, Zhouping Xin, Global classical solution to two-dimensional compressible Navier–Stokes equations with large data inR^2, Physica D, 376/377 (2018), 180-194.
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