On the Cauchy problem of 2D compressible fluid model with the horizontal thermal gradient effect

PDEs in connection with fluid mechanics (35Q35) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Strong solutions to PDEs (35D35) Diffusive and convective heat and mass transfer, heat flow (80A19) Compressible Navier-Stokes equations (76N06)

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