Asymptotic Stability of Explicit Blowup Solutions for Three-Dimensional Incompressible Magnetohydrodynamics Equations

[1]  Weiping Yan Dynamical behavior near explicit self-similar blow–up solutions for the Born–Infeld equation , 2018, Nonlinearity.

[2]  Binlin Zhang,et al.  Long Time Existence for the Bosonic Membrane in the Light Cone Gauge , 2013, The Journal of Geometric Analysis.

[3]  Ting Zhang,et al.  Global Small Solutions to a Complex Fluid Model in Three Dimensional , 2014, 1403.1085.

[4]  G. Hagedorn,et al.  An adiabatic theorem for resonances , 2010, 1002.1741.

[5]  Ping Zhang,et al.  Large Time Behavior of Solutions to 3-D MHD System with Initial Data Near Equilibrium , 2017, 1702.05260.

[6]  S. Alinhac,et al.  Existence d'ondes de rarefaction pour des systems quasi‐lineaires hyperboliques multidimensionnels , 1989 .

[7]  Weiping Yan,et al.  Existence of standing waves for quasi-linear Schrödinger equations on Tn , 2019, Advances in Nonlinear Analysis.

[8]  Li Xu,et al.  On Global Dynamics of Three Dimensional Magnetohydrodynamics: Nonlinear Stability of Alfvén Waves , 2016, 1603.08205.

[9]  Zhen Lei On axially symmetric incompressible magnetohydrodynamics in three dimensions , 2012, 1212.5968.

[10]  Fanghua Lin,et al.  Global Small Solutions to an MHD‐Type System: The Three‐Dimensional Case , 2014 .

[11]  Roger Temam,et al.  Some mathematical questions related to the MHD equations , 1983 .

[12]  Russel E. Caflisch,et al.  Remarks on Singularities, Dimension and Energy Dissipation for Ideal Hydrodynamics and MHD , 1997 .

[13]  P. Pucci,et al.  On solutions of space–fractional diffusion equations by means of potential wells , 2016 .

[14]  Giuseppina Autuori,et al.  Global Nonexistence for Nonlinear Kirchhoff Systems , 2010 .

[15]  Zhen Lei,et al.  Global Well-Posedness of the Incompressible Magnetohydrodynamics , 2016, 1605.00439.

[16]  Weiping Yan Nonlinear stability of explicit self-similar solutions for the timelike extremal hypersurfaces in $${\mathbb {R}}^{1+3}$$ , 2020 .

[17]  V. I. I︠U︡dovich The linearization method in hydrodynamical stability theory , 1989 .

[18]  Z. Yin,et al.  Local existence and uniqueness for the non-resistive MHD equations in homogeneous Besov spaces , 2016, 1607.08403.

[19]  P. Pucci,et al.  Approximation by regular functions in Sobolev spaces arising from doubly elliptic problems , 2020, 2005.10740.

[20]  Zhifei Zhang,et al.  Global well-posedness of the MHD equations in a homogeneous magnetic field , 2016, 1607.04397.

[21]  P. Feehan,et al.  Boundary-degenerate elliptic operators and Holder continuity for solutions to variational equations and inequalities , 2011, 1110.5594.

[22]  Birgit Schorkhuber,et al.  Stable blowup for wave equations in odd space dimensions , 2015, 1504.00808.

[23]  Yi Zhu,et al.  Global Classical Solutions of Three Dimensional Viscous MHD System Without Magnetic Diffusion on Periodic Boxes , 2017, 1701.07264.

[24]  Weiping Yan The motion of closed hypersurfaces in the central force fields , 2015, 1502.04786.

[25]  J. Moser A rapidly convergent iteration method and non-linear partial differential equations - I , 1966 .

[26]  L. Hörmander,et al.  The boundary problems of physical geodesy , 1976 .

[27]  Christiane Marliani,et al.  Evolution of current sheets and regularity of ideal incompressible magnetic fluids in 2D , 2000 .

[28]  J. L. Lions,et al.  Inéquations en thermoélasticité et magnétohydrodynamique , 1972 .

[29]  Sobolev regular solutions for the incompressible Navier–Stokes equations in higher dimensions: asymptotics and representation formulae , 2020, Rendiconti del Circolo Matematico di Palermo Series 2.

[30]  Weiping Yan On the explicit blowup solutions for 3D incompressible Magnetohydrodynamics equations , 2018, 1807.07063.

[31]  Nonexistence of Self-similar Singularities in the Ideal Magnetohydrodynamics , 2007, math/0703317.

[32]  R. Donninger On stable self‐similar blowup for equivariant wave maps , 2010 .

[33]  Ping Zhang,et al.  On the Global Solution of a 3‐D MHD System with Initial Data near Equilibrium , 2015, 1511.02978.

[34]  H. Alfvén,et al.  Existence of Electromagnetic-Hydrodynamic Waves , 1942, Nature.

[35]  James C. Robinson,et al.  Local existence for the non-resistive MHD equations in Besov spaces , 2015, 1503.01651.

[36]  P. Pucci,et al.  A Liouville-type theorem in a half-space and its applications to the gradient blow-up behavior for superquadratic diffusive Hamilton–Jacobi equations , 2019, Communications in Partial Differential Equations.

[37]  Vicentiu D. Rădulescu,et al.  Global small finite energy solutions for the incompressible magnetohydrodynamics equations in R+×R2 , 2021 .