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  1. On the Cauchy Problem for the Equations of Ideal Compressible โ€ฆ

  2. On the Cauchy Problem for the Equations of Ideal Compressible โ€ฆ

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    For each , the Cauchy problem of the 3D ideal MHD (1.3) admits a solution that ceases to be regular in nite time. Let T be the largest time such that the solution 2 C1 3 R [0; T ) . The following statements hold: forms at T . And as ! 0, we have T ! 0. This means that the constructed initial data ( )
    arxiv.org/pdf/2110.10647.pdf
    Compressible magnetohydrodynamics (MHD) system is used to describe the macroscopic behavior of the electrically conducting fluid in a magnetic field. The application of MHD has a very wide of physical objects from liquid metals to cosmic plasmas. The system of the 1-D resistive MHD equations has the form:
    link.springer.com/article/10.1007/s10440-021-00434-1
    The 2D ideal compressible MHD system takes the form: R is the magnetic eld intensity, S is the entropy and p is the pressure satisfying the equation of state p = p(%; S): We consider the polytropic gas. The pressure p(%; S) obeys the following equation of state where A is a positive constant and > 1 is the adiabatic gas constant.
    arxiv.org/pdf/2206.14003.pdf
    To the best of our knowledge, this is also the rst nonlinear result of low regularity ill-posedness for the 3D ideal compressible MHD. In the absence of the magnetic eld, we also provide a desired ill-posedness result for the 3D compressible Euler equations.
    arxiv.org/pdf/2110.10647.pdf
  4. On the Cauchy problem for the equations of ideal compressible โ€ฆ

  5. On the Cauchy Problem for the Equations of Ideal Compressible โ€ฆ

  6. Global Strong Solutions to Cauchy Problem of 1D Non-resistive โ€ฆ

  7. On the ideal compressible magnetohydrodynamic equations