Associated Project 6 • Stability and instability in fluids and materials

In our research we consider physically motivated problems in partial differential equations, which combine physical effects and interesting mathematical phenomena.
Two particular points of focus here are the role of mixing and resonances in fluids and microstructures in materials.

Publications

  1. . Linear inviscid damping in Sobolev and Gevrey spaces. Nonlinear Anal., 213:112492, December . URL https://doi.org/10.1016/j.na.2021.112492. [preprint] [bibtex]

  2. and . Echo chains as a linear mechanism: norm inflation, modified exponents and asymptotics. Arch. Rational Mech. Anal., 242(1):643–700, October . URL https://doi.org/10.1007/s00205-021-01697-6. [preprint] [bibtex]

  3. , , , and . On a probabilistic model for martensitic avalanches incorporating mechanical compatibility. Nonlinearity, 34(7):4844–4896, June . URL https://doi.org/10.1088/1361-6544/abfca9. [preprint] [bibtex]

  4. . On enhanced dissipation for the Boussinesq equations. J. Differential Equations, 282:407–445, May . URL https://doi.org/10.1016/j.jde.2021.02.029. [preprint] [bibtex]

  5. . On the Boussinesq equations with non-monotone temperature profiles. J. Nonlinear Sci., 31(4):64, 38, May . URL https://doi.org/10.1007/s00332-021-09723-3. [preprint] [bibtex]

  6. . On echo chains in Landau damping: traveling wave-like solutions and Gevrey 3 as a linear stability threshold. Ann. PDE, 7(1):1–29, January . URL https://doi.org/10.1007/s40818-020-00090-y. [preprint] [bibtex]

  7. and . On the smallness condition in linear inviscid damping: monotonicity and resonance chains. Nonlinearity, 33(11):6176–6194, October . URL https://doi.org/10.1088/1361-6544/aba236. [preprint] [bibtex]

  8. , , , , and . Exact constructions in the (non-linear) planar theory of elasticity: from elastic crystals to nematic elastomers. Arch. Ration. Mech. Anal., 237(1):383–445, July . URL https://doi.org/10.1007/s00205-020-01511-9. [preprint] [bibtex]

Preprints

  1. and . On echoes in magnetohydrodynamics with magnetic dissipation. CRC 1173 Preprint 2023/5, Karlsruhe Institute of Technology, January . [bibtex]

  2. . On stability estimates for the inviscid Boussinesq equations. CRC 1173 Preprint 2022/72, Karlsruhe Institute of Technology, December . [bibtex]

  3. and . On variable viscosity and enhanced dissipation. CRC 1173 Preprint 2022/71, Karlsruhe Institute of Technology, December . [bibtex]

  4. . On echo chains in the linearized Boussinesq equations around traveling waves. CRC 1173 Preprint 2022/70, Karlsruhe Institute of Technology, December . [bibtex]